Ultimately, I don’t think it makes any legal difference how the nonprofit handles the situation. 

(I am assuming the nonprofit is a charity although “nonprofit” is not synonymous with “charity.”  See Ready Reference Page: “What Do We Mean When We Say ‘Nonprofit?’’). The one thing a charity can not do is to pay the teacher on the basis of the “profit” from the classes.  As long as the payment is based on the revenue, and not the net, a charity is permitted to make a payment so long as it is not excessive.  There is nothing in your question to suggest that the per/student fee would not be within the range of reasonableness for the program. 

As a “nonprofit,” the organization also can’t use its status to provide private inurement to the instructor, but that would seem require a lot more benefit than the ordinary income from a student to take an educational course.

If I were the administrator of the nonprofit, I would much rather collect the fees and pay the instructor either a fixed fee or a per/student fee.  I would rather have control of my own program than leave it up to the instructor to run.  Being a good teacher does not necessarily equate to being a good, or fully communicative, administrator.