English tag questions have so many forms, I doubt I could do the topic true justice in an answer. Essentially, as written, this is a 'unbalanced tag question'.
In this particular instance it does feel like the 'wrong' choice. I would have expected "mustn't we?" rather than "must we?"
Having listened to it a few times, & I'm now convinced she actually does say "mustn't we?" she just clips it tight, almost entirely burying the "n't". The guesswork captioning gets it wrong, but in this instance, I'm not truly surprised.
In the video, the entire conversation is positive. As written in your question, you would expect some form of disagreement/resentment which would make the unbalanced form valid.
I have to admit I don't know the show, so I don't know the relationship the characters have, but watching the clip validates that she does in fact say "mustn't".