Your TA Supervisor is the faculty member for whom you are a TA. Each faculty member runs their class differently and you should expect each experience to be different.
As with your other advisors, a key aspect to a good experience with your is to keep communications open. It is strongly suggested that you set up regular meeting with your advisor. You should plan to meet with (or at least contact) your TA Supervisor before the start of classes at the beginning of a semester. (Showing up in your TA Supervisor’s office for the first time 15 minutes before the first class meeting of the semester is not a good way to start the semester.) Also, if you are scheduled to meet with your recitation section before the first meeting the professor has with the students, do not assume that the class is canceled.