The events depicted in it are described at length in Wayne Cooper's biography of Claude McKay as well as in James' more recent book. Cooper gives the publication information as April 6, 1912, and indicates that the poem was published in the Daily Gleaner -- though he does not indicate a page number (in every other instance he gives accurate and exact page numbers for the poems and articles he sites).
But there is no hint of the poem in the April 6, 1912 edition of the Daily Gleaner. I have looked at the entire run of the Gleaner in the year 1912 in the collections at the U.S. Library of Congress, and have not found the poem published there. Maxwell in his own note on the poem corroborates that the poem appears to be missing from the Gleaner: "My own examination of the Gleaner's run from 1911 through 1912 did not uncover any printings of the poem, though Max Eastman's introduction to Harlem Shadows and Winston James' Fierce Hatred of Injustice concur on McKay's authorship.
Given the absence of any original evidence of the publication of this poem, it seems more correct to indicate that the original publication venue is unknown.
Despite the publication mystery, it does not seem appropriate to challenge the claim that McKay authored this poem, in part because Max Eastman made an oblique reference to it in his 1922 introduction to Harlem Shadows:
With the blood of these rebels in his veins, and their memory to stir it, we cannot wonder that Claude McKay’s earliest boyish songs in the Jamaica dialect were full of heresy and the militant love of freedom, and that his first poem of political significance should have been a rally-call to the street-car men on strike in Kingston.
Moreover, the theme of the poem reflects a budding political radicalism that can also be seen in poems that were published in Jamaican newspapers in 1912, like "Christmas in De Air." And, there is a reference to riding the tram in at least one poem in Songs of Jamaica. However, we need more information about its publication venue to confirm McKay's authorship and the publication context -- especially since scholars like Cooper, Winston James, and Josh Gosciak have all written about this poem at length in their respective analyses of McKay's poetry.
A brief note on the historical context: Cooper describes at length the "Passive Resister" movement that erupted in Kingston in the spring of 1912 following the tramway's decision to raise fares. Riders protested by refusing to buy tickets in bulk, and instead bought individual tickets with the smallest possible currency to beleaguer conductors. Some of the protests did turn violent, leading to strong suppression from authorities. However, the aspiration of the leaders of the "Passive Resistance" movement was to nonviolently object to what they saw as an unjust fare. Both Maxwell and Cooper describe the poem as an important precursor to the kinds of social-justice themed poems he would write after moving the U.S. Here is Cooper along those lines: "McKay's passionate assertion of the right of self-defense anticipated in tone and substance the militant protest poetry he would later write in the United States. McKay's highly developed sensitivity to injustice made him a potential rebel in Jamaica, long before he became aware of American racial prejudice" (Cooper, 53).
Cooper also indicates that there's "no evidence to indicated that McKay actually participated in any of the demonstrations in February" (53).