There doesn't seem to be a standard. I asked before surgery who my body would belong to after surgery. The answer was: surgeon 30 days, cardiologist next 3 months, back to primary after that.
The day of the surgery, my surgeon was committed to my care and also supportive to my husband when it seemed a problem was developing. He went on vacation right after my surgery, but I received excellent care from his practice. The followup appointment one month after surgery was with the nurse practitioner.
You need to find out who to contact with concerns in the weeks after surgery, but it may not be the surgeon himself.
Best wishes!