That's right. A mastermind has to be among the participants. It was created that way from the start, much like a traitor can't operate from the shadows. They are subject to the same rules as anyone else.

There would have been an execution if she had voted for. Then the game would have ended and one of you wrapped up in the hangman's noose with the executioner's axe in hand.

[She shakes her head slowly, looking at first like she might say I don't know.]

Either by irony or design, the rules for the role of mastermind are rather restrictive.

A mastermind can not reveal who they are. Unless found out by someone else. They can not reveal a culprit or victim themselves. It would be rather unfair, they see everything. Including every conversation taking place at any moment. Nor can they reveal any truths about the town.

Thus the traitor role made by the mastermind to do what they can not.