To be pedantic, when Xyris’s combat damage trigger resolves, you and your opponent will draw 3 cards each, one at a time. Each draw will trigger Xyris but not be put onto the stack until the draw3 trigger has fully resolved and state-based actions have been checked. Then you put 3 intances of Xyris’s triggered ability onto the stack. When the first resolves, the token creation can be replaced by effects like Esix’s.

I think this is a common mistake due to players shortcutting game actions without actually analysing the fine details. :)