ShiroKuro To be fair to your teacher, I wouldn't do it normally. Sophia's part is the easier of the two to keep rhythm. But it made more sense for me to record first because she has more rests and because it's easier to get a good melodic interpretation while listening to the harmony. So our plan was that I record with strict rhythm, then temporarily overlay a metronome beat to help Sophia create her recording. (Ultimately, she saved us time and effort by recording before I overlayed the metronome).
Now, for your recording, I say if it sounds good, and it's something you could actually do in a live performance, go for it! Anyways, I don't have any idea how to contact your teacher to report your misbehavior.