Very simply, if you are qualified to fly the ac and you are doing so under the supervision of even a 'spotty kid who needs the money'(sic) then you should log it as P1S. The 'spotty kid' who happens to be qualified as a Flight Instructor is the Commander and logs P1 - and he/she directs the content of the flight. You do not.
Anyway - does it really bŁoody matter?
I will - as Formation Flyer will shortly find out - be standardising the matter for anyone who flies from my RF. If they don't like it, byeeeeeee.......