Hi there
It really depends on the practice. However basically certain dosages of chemical peels can only be purchased and ordered by clinics/doctors, and these are what we term as prescription only peels.
They tend to be of a higher concentration/risk of adverse outcomes if poorly used.
I suspect your derma did the first few treatments to ensure that the dose is safe and to ascertain your skin reaction first, and then beyond that the mechanical application is done by the assistant.
You may want to ask your derma when you next visit, and he/she may oblige by assuring you and providing some education on the peels being used.
Winston