a) the demonstrations started already at the end of 1919 and that's when the Zionist Commission requested Ze'ev Jabotinsky to assume the command of a local Jewish defense group, which became known as the Hagana.
An Arab history, but with good sources, points out, for example,
An undercover agent of the Zionist Intelligence reported a meeting of sixteen members of el-Feda 'iyyeh on 27 August 1919, presumably in preparation for a revolt.
And this, too:
During September British Naval Intelligence reported that anti-Zionist feeling was becoming increasingly bitter and that 'a plot has been discovered by us by which it was proposed to assassinate Dr. Weizmann on his arrival'. On announcing the separation of Palestine from Syria towards the end of September vehement protests were voiced in Jerusalem's Suriyya al-Janubiyya (Southern Syria), which was owned and edited by 'Aref al-'Aref, and in the Damascus press. The announcement inspired an article by 'Izzat Darwaza in al-Urdun (The Jordan), published in Damascus, appropriately entitled 'Now is the Time to Act': "It is not for the representatives of English, French and Zionist affairs to do as they please with a country which has been liberated by the blood of its children, who are ready to shed more blood if necessary to attain their ends".
Another Naval Intelligence report noted that by November 1919 the whole anti-Zionist movement in Palestine had taken a very anti- British turn. Four weeks later Naval Intelligence reported that anti-Zionist propaganda was spreading to small villages where the fellaheen are interested listeners when local and Damascus papers are read out to them.
b) the mandate process was a bit different than just this
The British occupied the region, but the Mandate was not officially recognized until the San Remo Resolution of April 25, 1922.
February 3, 1919 - The Zionist organization submits a draft resolution to the Versailles Peace Conference and the final decision of the Conference was that the former Arab provinces of the Ottoman Empire should be separated from it and the newly conceived mandate-system applied to them and included five main points foremost the recognition of the Jewish people's historic title to The Land of Israel and their right to reconstitute their National Home in Israel.
April 25, 1920 - San Remo Conference, an international meeting of the post-World War I Allied Supreme Council, attended by the four Principal Allied Powers (and the United States acting as an observer). It adopted a resolution which included the Balfour Declaration in its entirety - in shaping the map of the modern Middle East, which was subsequently approved unanimously by the fixty-one nations members of the League of Nations. That decision confirmed the mandate allocations of the First Conference of London (February 1920) and thus became the basic document upon which the Mandate for Palestine was later constructed.
August 10, 1920 - Adoption of the Treaty of Sevres which included Article 95 whereby the High Contracting Parties agree to entrust, by application of the provisions of Article 22, the administration of Palestine, within such boundaries as may be determined by the Principal Allied Powers, to a Mandatory to be selected by the said Powers as per the language of the Balfour Declaragtion.
March 28/29, 1921 - Continuation in Jerusalem of the Cairo Conference when Winston Churchill, Colonial Secretary, proposed giving Feisal, instead of the throne of Syria, the throne of Iraq, and at the same time giving Feisal’s brother Abdullah the throne of Transjordan. Installing an Arab ruler in Transjordan, he presumed, would enable Western Palestine—the area from the Mediterranean Sea to the River Jordan, which now comprises both Israel and the 'West Bank' — to become the location of the Jewish National Home under British control, in which, in Churchill’s words, the Jews were to go “of right, and not on sufferance.” Earlier TE Lawrence explained to the senior officials gathered there that the presence of an Arab ruler under British control east of the Jordan would enable Britain to prevent anti-Zionist agitation from the Arab side of the river. In support of this view, Lawrence himself told the conference, as the secret minutes recorded: “He [Churchill] trusted that in four or five years, under the influence of a just policy,” Arab opposition to Zionism “would have decreased, if it had not entirely disappeared.”
[UPDATE: from Martin Gilbert: "On March 27, 1921, ten days after Lawrence’s suggestions in Cairo, Churchill sent him from Jerusalem to Transjordan to explain to Abdullah that his authority would end at the eastern bank of the River Jordan; that the Jews were to be established in the lands between the Mediterranean and the Jordan (“Western Palestine”); and that he, Abdullah, must curb all anti-Zionist activity and agitation among his followers.The next day, in Jerusalem, Lawrence, Churchill, and Abdullah were photographed at British Government House: Churchill bundled up against the cold, Lawrence in a dark suit and tie, Abdullah in army uniform with Arab headdress.
At their meeting that day, Abdullah agreed to limit the area of his control to Transjordan and to refrain from any action against the Jewish National Home provisions of the Palestine Mandate west of the Jordan.
Lawrence had thus helped ensure that the building up of the Jewish National Home could continue. He already knew that national home’s potential: Twelve years before the Cairo Conference, while traveling through the Galilee around Tiberias, he reflected on the glory days of the region in Roman times, and on the Jewish farm settlements he saw on his travels. Writing home on August 2, 1909, he explained, “Galilee was the most Romanized province of Palestine. Also the country was well peopled, and well watered artificially: There were not twenty miles of thistles behind Capernaum! And on the way round the lake they did not come upon dirty, dilapidated Bedouin tents, with the people calling to them to come in and talk, while miserable curs came snapping at their heels: Palestine was a decent country then, and could so easily be made so again. The sooner the Jews farm it all the better: Their colonies are bright spots in a desert.”. and see this post.]
June 3, 1922 - British Policy Statement on Palestine (the 'Churchill White Paper'). In this explanation, Britain told informed ‘we (British Administration) never gave an authority for creation of Jewish Palestine to Jews, we promised only building of national home for Jews in Palestine'.
July 24, 1922 - The League of Nations approves the draft British Mandate for Palestine. British express interest in Zionism, and describe their main intent of developing a Jewish National Home.
September 16, 1922 - The Council of the League of Nations accepts the British Transjordan memorandum defining the limits of Trans-Jordan and excluding that territory from the provisions in the Mandate concerning the Jewish national home.
September 21, 1922 - The US Congress passed a joint resolution sponsored by Lodge-Fish stating its support for accepting the 'establishment of Jewish national home in Palestine’ using the exact language of the Balfour Declaration.
September 29, 1923 - British Mandate for Palestine and French Mandate for Syria come into operation with TransJordan as territory excluded from unspecified provisions of the Mandate.
December 3, 1924 - adoption by the US Congress of the Anglo-American Convention on Palestine by which United States agreed to the British administration of Palestine pursuant to the Mandate and imposing a solemn obligation on the US Government to protest any British violation of this treaty, which had repeated every word, jot and tittle of the Mandate Charter in the preamble of the Convention, regardless of whether the violation affected American rights or those of the Jewish people.
Arab opposition began in early 1919:
The first Palestinian Arab congress (al-Muʾtamar al-Arabi al-Filastini) met in Jerusalem from 27 January to 9 February 1919. Organized by local Muslim and Christian associations, its thirty participants framed a national charter that demanded independence for Palestine, denounced the Balfour Declaration (and its promise of a Jewish national home), and rejected British rule over Palestine. A majority sought the incorporation of Palestine into an independent Syrian state, and the delegates strongly denounced French claims to a mandate over Syria. The congress expressed its request for independence in the language of U.S. president Woodrow Wilson's principles supporting the right of self-determination of subject peoples.
This, of course, highlights the major problem with the so called "Palestinian nationalism" in that in the early 1920s, it sought not an "independent Palestine" but a "Greater Syria".
The text of two of the relevant decisions"
1. We consider Palestine as part of Arab Syria as it has never been separated from it at any time. We are connected with it by national, religious, linguistic, natural, economic and geographic bonds.
2. The Declaration made by M. Pichon, Minister for Foreig Affairs for France, that France had rights in our country based on the desires and aspirations of the inhabitants has no foundation and we reject all the declarations made in his speech of 29th December 1918, as our wishes and aspirations are only in Arab unity and complete independence.
3. In view of the above we desire that one district Southern Syria or Palestine should not be separated from the Independent Arab Syrian Government and to be free from all foreign influence and protection.
Here's another picture which may be from late 1919 or early 1920: