Epochrasite dies under opponents control
Hi,
Thanks for your question. If a card isn't on the stack or on the battlefield, it only has an owner, it can't be controlled by another player. Even if Epochrasite is controlled by the opponent when it dies, once it's in exile and suspended, it only has an owner, and that would be AP. The triggered ability that triggers when Epochrasite died is controlled by the NAP (since NAP controlled it when it died), but it's under AP's ownership when it's in exile and suspended.
At the beginning of AP's upkeep, they'll remove a time counter, and when the last time counter is removed, AP casts the spell and it enters under AP's control. Other than exiling it from AP's graveyard when the dies trigger resolves, NAP won't have anything to do with Epochrasite after it dies, because they're not the owner of the card.
Thanks,
Nathan Long
Magic Rules NetRep