When playing in the Amonkhet prerelease something that was being played a lot were cards with exert which temporarily buffs a unit at the cost of it being tapped for an extra turn. Paradox Engine's ability is "Whenever you cast a spell untap all your creatures. Will creatures with exert become untapped or will they stay tapped?
Exerting a creature keeps it from untapping only during the next untap step of the player who exerted it (C.R. 701.37a), and not at any other time (including during other untap steps). (Note that "exert" is a keyword action, not an ability -- the rule for exerting appears in C.R. 701, "Keyword Actions", not C.R. 702, "Keyword Abilities".)
EDIT (May 11): Clarification.