The human brain is wired in such a way that when someone sings it does not really consider the octave, but if a note is high or low. In unison singing male voices will default to singing the same line an octave lower than female voices, and will repeat in their own octave. This is important when giving notes in choir conducting or vocal coaching, so you don’t give the actual sounding pitch, but (for a female voice conductor or coach) the male voices in the upper octave or (if you are male voice) the female voices in the lower one.1
It is actually easier for a singer to take the pitch of a singer of opposite sex if the other singer sings up or down an octave (in their own “natural” pitch). Artificially trying to sing the pitches high to female singers or low to male singers is probably going to cause confusion and will have them take the note less safely.
But it is very important that this only applies when giving the pitch to a singer of opposite sex. It does not apply when giving notes on piano or any other instrument. And this is something every trained choir conductor and vocal coach should know. When singing you change the octave to your own natural pitch, but when giving pitches on an instrument you give true pitch.
So what is happening is that your teacher is giving the notes on the piano that would correspond to her natural pitch, and is expecting you to take the pitch as if she had sung it. But truly she should be the one playing the piano in your natural pitch.
If you hadn’t said that she was extremely accomplished and professional I would simply suspect that she was an inexperienced teacher. But that way ... I suppose maybe she in not a trained vocal teacher, but a trained singer who gives lessons to make a living (as many trained musicians do). Then she might also mostly have female students, making her inexperienced with male singers.
Then, once you are more experienced as a singer your brain will have learned to pretty much ignore the octave of an instrument when taking the pitch, as you tend to know the general range of what you are about to sing, and instrument cues can go from very low to very high.
1 And by female and male I here mean natural Soprano/Alto and Tenor/Bass voices, I am totally aware that there are things such as perverted mutation2 as well as transgender and non-binary people.
2 That is a rare occurrence where the voice does not change as typical for the sex, i.e. a girl growing a larger larynx or a boy growing a smaller one.