Electrically, it sounds correct if I follow you correctly.
I wonder about the duct for the fan. Did he run a duct from the new fan to the outside? I assume there wasn't already a duct there as it sounds like there was no fan in this bathroom previously. He may have installed the fan without the duct to let you install the duct yourself or by someone else. You will want to check that out as you don't want to just blow the mosit air into the attic.