To me the deck of many things is clearly intended to work only with PCs or NPCs with class levels since it manipulates XP, hence I wouldn't allow it to work for other creatures. Plus, the wording is lacking the magical words:"the creature that draws this card" or "a creature that draws from this deck" or "a card drawn by a creature" which is a popular wording to determinate who can activate something.
But having someone else under your control drawing from the deck sure will prevent bad things from happening to you.