That isn't how Emergency Powers works at all. All of the Addendum parts are part of the spell's resolution. There is no trigger anywhere in the text for the "put a permanent with CMC <= 7 into play" part of the card; it's a second effect to the spell that you get for casting it during your main phase.Quote from endgame1331 »Interesting thing to note is that Addendum is a cast trigger a la cascade and the eldrazi. So even if the spell is countered, the addendum is still enforced. In the instance of the timetwister, pushing a busted permanent like Teferi through countermagic sounds pretty good.
For it to function like Cascade and the Eldrazi, the text would have to be something like this:
Each player shuffles his or her hand and graveyard into their library, then draws seven cards. Exile Emergency Powers.
Addendum -- When you cast this spell, if you cast it during your main phase, you may put a permanent card with converted mana cost 7 or less onto the battlefield.