I was never clear as to how this riot started - (and it's still a bit sketchy to this day):
Without warning a number of armed Negroes under the lead of obnoxious and dangerous men of their race proceeded through the downtown business section of Tulsa to the courthouse and began a demonstration of defiance and lawlessness. They were advised that no attempt was being made to lynch the Negro prisoner and retired from the scene, only to return later with apparent reinforcements, many of them armed with pistols .and guns and one body of them were marching in columns of fours, showing military, or at least recent organization and drill. Insulting demands were made by these Negroes on the peace officers, a shot or two was fired and a race riot immediately started. The Negroes began firing indiscriminately and before they vacated the business section several white men and several Negroes had been killed.
The timeline link paints a somewhat different picture, but the “flashpoint” was unquestionably the meeting of two mobs outside the court house.