When an aircraft carries two or more pilots as members of the operating crew one of them shall, before the flight commences, be designated by the operator of the aircraft as Commander....
A pilot flying as 'Pilot in command under supervision' shall enter flight time acquired in this manner in the 'Pilot in command' (P1) column and the P1(U/S) column. In each instance the Commander of the aircraft must certify the entry.
Where an aircraft is certified for operation by either a three pilot or two pilot plus flight engineer crew and the operator opts to fly the aircraft with three pilot the 'third' pilot, who must be properly rated on type, is designated 'Systems Panel Operator' (SPO).
Conclusion:?
On line training therefore, if in the left with LTC in right, one logs the lot as P1and P1(U/S) and gets the LTC, the operator's Commander, to certify the entry.
If the LTC is in the jump seat then he must be out of the loop and no P1(U/S) entry need be made.
Does that make sense? That's what I have always done, although I must admit that I've never bothered to get the LTC to certify the entries and no one has ever asked me about it.