You should be able to use Damage Dealer components as a means to apply that I believe. The Action RPG tutorial should show you an example (it has a grenade if I remember correctly) of how to set it up, then you can just setup the rest of the battle normally and it should transfer as its the same combatant.
Personally I would think on the first attack, otherwise you effectively create a hybrid system where you can avoid turn based battles entirely by continually firing projectiles / waiting for cooldown or reload, and so on. In my experience with a system, you run into some really weird pitfalls and it ends up that neither side ends up feeling good.
Starting on the first attack (but giving the attacker some kind of advantage for it) is pretty common, but again that's all in my opinion. Its your game, so whatever is fun to you is what matters :)