The mitzvah of ‘terumas hadeshen’ [taking away ashes from the mizbeiach] was done everyday when the crier called out or a little before or after. On Yom Kippur it was done at midnight and on Yom Tov it was done at the first watch. [Watches are a concept derived from the fact that in shamayim at different intervals during the day different malachim come on duty to say shira.]

Before the crier called out on Yom Tov, the azara was full with people.

Yuma 2:1

Originally, whoever would want to do the terumas hadeshen would go do it. If there were many who would want to do it, they would run up the ramp of the mizbeiach and whoever reached within 4 amos of the mizbeiach first won. If 2 reached it at the same time, the officer would tell all of the cohanim to put out a finger or two (excluding the thumb). This was to make a lottery.