I am not asking about the basics here: I know it comes out of speed + random value.

What I am wondering about is if the turn order for specific round is determined before it starts or rather dynamically.

For example: I have Jester with speed buffs that manage to go first. If he buffs my party members with speed, does it affect them in this case for the current round?

I believe it does. But like you said, that random factor might make it seem like it doesn't sometimes.

In my experience, the speed buff starts "working" next round, meaning the turn order is already determined once the round starts. Not 100 % sure yet though.

okay then.. nobody knows for sure?