For instance I want to cast Shock on Barkhide Troll during my main phase. Then my opponent can respond to it with Troll activated ability. If I understand it correctly - he had to use Troll's Active Ability before my instant had targeted the creature. So it means my instant should deal the damage.
It is like when you want to use an ability which says "your creature can't be blocked until the end of the turn" and if you use such an instant after an opponent blocked your creature - an instant won't work because you had to use it when you assigned attackers