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.

https://acoup.blog/2022/06/03/collections-total-generalship-...