We know that the Twili were actually sealed, because they are sealed in the Twilight Realm in the game.

If the Interlopers pissed off the goddesses by trying to take over the Sacred Realm, why would they be banished to the Sacred Realm?
They are clearly two different places.

The entrance to the Twilight Realm is said to be the Twilight Mirror.
The entrance to the Sacred Realm is said to be the Temple of Time.

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Bomber's Notebook | Zelda Informer, Home of The Bombers | Theorizing Resources | Aralith's OoT Retelling
Voted as Best Zelda Theorist in the Summer '08 Awards. Thank you to all who voted, and to all who inspired me along the way!