Ambuscade's Traps

Say you come across one of Ambuscade's traps and you reschuffle it back into his deck face up.  Later on during his villain turn you draw a card and the card under it is a face up trap.  Does the trap go off immediately before the drawn card is played?  Do you play the drawn card then the trap goes off?  If so, what if at the end of the card drawn it says reschuffle the villain deck?  Does the trap then not get triggered?

The Traps go off even on Wraith's Infrared Eyepiece reveal. Hence, it implies going off upon the draw revealing it, prior to resolving the card text.