The language of an object interaction in the PHB seems important here: "You can also interact with one object or feature of the environment for free, during either your move or your action" (p.190). The object interaction, while not costing your action or movement, does happen as part of them (which is important so that someone who's paralyzed can't open a door for example, since incapacitate doesn't specify anything about free actions). This means that the condition for AoO exempt movement, "something moves you without using your movement, action or reaction" is not met, and an AoO can be taken.
Combined with the fact that the AoO section specifically says "an explosion hurls you out of a foe's reach or if gravity causes you to fall past an enemy." It says "out of reach" for one and "past" for the other, makes me think you would in fact provoke an opportunity attack in this situation.