Kraven’s power should fire in the first turn of a fight against Rocket. Rocket’s power fire’s “at the start of the battle”. The battle starts before the turn.
Edit: I know the mechanics don’t allow powers to fire on the very first turn of the game for balance, but you may want to reconsider, or alter the mechanics or wording for Kraven to allow this. He does need a boost. D3 could help him start a coonskin cap business.