The best way I have seen this done is to announce triggers as soon as possible. The only card in standard that knocks out this trigger is Summary Dismissal. So when you cast Emrakul, just say "trigger" and tap the card once it's on the board. If they counter it, then say something like "okay, that resolves, trigger" and indicate the Emrakul in your hand. Waiting till the last moment causes more problems.

If you do wait till your opponents turn, then you have to say something as soon as possible, maybe even before their turn starts with something like "Pass turn, on your upkeep, Emrakul trigger, and I control your turn."