No, she's facing the right way - it's a music lesson, so she's facing the instrument which she's playing. But she's looking slightly towards the (I assume) teacher, as if asking "Am I doing this right?". On Tim's version, she has abandoned the instrument completely and is just talking to the gentleman, who is also much more engaged with her judging by the body postrue - I'd say even there's something else than music lesson going on in that version :) So these paintings, while being similar, actually depict two quite different situations.

She is facing the right way but her reflection in the mirror isn't.

It looks to me that their heads are pointing in about the same direction (looking at the man) but in Vermeer's she is turning her head (her body is facing another direction)