Now, in your case, I believe it is different. You are paying a private teacher and in this case the teacher should adjust to your schedule. If he has a problem with this then the teacher - student relationship is not balanced and the collaboration shall be ended.
However, I believe this shall be discussed witht the teacher beforehand. He should know what time you are willing and can spend on excersizes, so that he can schedule is lessons on this.
Just discuss with the teacher and I am sure you can work something out.
Regards,
Jan