Can opponents keep Jeskai Infiltrator under their control past the end of their turn if it was manifested?
Yes, they will keep control of Jeskai Infiltrator. The card was exiled and then returned to the battlefield, so it is considered by the rules a new permanent with no relation to the card that Act of Treason was used on.


  400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. There are seven exceptions to this rule:


(none of the exceptions apply here).

Remember that everybody will know which of the face down cards is Jeskai Infiltrator, because who is the owner of a card is always known. There is a ruling in Jeskai Infiltrator that confirms this.