The rule applies. In the FAQ there is this:
Q. Does the "2.6 seconds rule" apply to defeating a monster without killing it, or just to killing it?
A. Any sort of defeat. If you defeat it without killing it, other players still have about 2.6 seconds to play an applicable card to frustrate you.
And this:
Q. Some cards, like Magic Lamp, Illusion, and Pollymorph Potion, let you get rid of ONE monster. If you get rid of a monster, does its mate (or, in the expansion, its relatives) also leave? In other words, is Mate an enhancement card like Ancient or fully separate like Wandering Monster additions?
A. A Mate is like a Wandering Monster. There are now two monsters, and you have to get rid of them individually. If you play the get-rid-of-it card before somebody plays Mate, though, there's no monster left for the Mate to join, so Mate can't be played.
Wandering Monster (plus another Monster) would be included in that first Q&A. I included the other to give you an indication on one given situation of a card that would not apply.