Q: If I’m the one who played the UnGoal that ended the game, can I play the Secret Cultist to win the game?

or is that considered to be playing it “during my turn”?

A: If an Ungoal is played, and conditions are met, then it suddenly becomes no-one’s turn, as the game is essentially over, and anyone, including the person who played the Ungoal, can then reveal the Secret Cultist to claim victory.