Instant
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As the Decoy Gambit resolves, first the next opponent in turn order (or, if it’s an opponent’s turn, the opponent whose turn it is) chooses whether you’ll draw a card or return their creature that was targeted to its owner’s hand, then each other opponent in turn order does so knowing the choices made before them. After all choices are made, you draw the appropriate number of cards. After you’ve drawn, the appropriate creatures are all simultaneously returned to their owners’ hands.
For each opponent, if you didn’t choose a target creature they control or if that creature has become an illegal target, that player can’t choose for you to draw a card.
If a creature targeted by Decoy Gambit changes controller, it’s no longer a legal target.