She's been living in Ponyville for a while; it had been hard for her to accept Twilight's offer, but she'd agreed anyway (she'd nowhere else to go, after-all). Time passes and she realises, no matter how kind and friendly the residents of Twilight's castle are, she does not belong in such rowdy a place.

Canterlot Castle had been the obvious other option, and it's quite an adventure, of that Tempest can be sure, she just didn't realise she'd come out of this with something more than new friends.

(Spoiler—or not really: Celestia x Tempest endgame.)