INLAK, congrats on your first flight! And you already expect to seat on the left? Come on...
Seriously, in my company it is the same. The PIC has the rating and that's it. As far as I know, they could let you legally land "under supervision", but would carry full responsability (don't ask me if that's anymore than usual, though). We have some PICs letting the poor F/O try one once in a while, but I have yet to meet one! It could be that my normal way of flying make them hesitant