From my understanding, disabling a card doesn't stop the effect once it's been activated, it just prevents the effect from being reused again until it's re-enabled. It'd work the same as if you disabled Sulu or Data or any other "Action:" card, the effect has already happened - the source is irrelevant. Like shooting a guy -after- he throws a grenade doesn't stop the grenade.
This seems correct. Also, consider something like Gowron's Action text being used on the turn his ship is destroyed. Although removed from play, his action's effect remains until the end of the round. Allied Klingon ships he targeted would still receive their +1 attack die.