I bet you all thought this was a question about PCing the roll to trigger Earthquake, didn't you?

The question is, since Earthquake is damage dealt, Impervious applies (along with Toughness, Mastermind, and Invulnerability). So are you allowed to PC that Impervious roll? Your own if it happens at the start of your turn and your opponent's if at the start of their turn, naturally.

Yes, Impervious has the potential for a re-roll against Earthquake damage---as you said, assuming that it is your Impervious figure on your turn, or your opponent's Impervious figure on his turn.

coolness!!