It doesn't matter who deals the killing blow. If a creature dies while subject to the necrotic damage effect, it gets reanimated; this applies even if the creature has enough necrotic resist to negate the damage, or dies outside the 20-square range limit. Good thought though.
You could try to work something where you tag stuff with the necrotic damage and then throw the Sword into the sun before the target actually dies, but you'd have to be fighting in the mouth of a cave or some such... though I suppose the PCs might start trying to lure every monster in a dungeon up toward the entrance. I'll have to ponder that.
