The author has an entire series of posts on how pre-modern generalship did and didn't work, including a post on issuing commands. The tl;dr is that there cannot have been a generalized order to fire on cue because pre-modern armies didn't have that kind of command resolution and speed. Best case you have a few guys who start firing because they're told to and the rest follow suit when they notice that it's started, more likely there's an established doctrine for when firing should happen and archers use their judgement for whether to start.
I don't think a command to start firing is that complicated. A simple flag wave suffices especially for <100 archers that's standing still. There are more complicated commands that a centurion had been able to do.
https://acoup.blog/2022/06/03/collections-total-generalship-...