Like Gus, I interpret the rules as indicating that there are two possibilities. But I don't agree with him about what those possibilities are!
The first choice, as Gus says, is that the instructor logs P1 and you log PUT.
The second option is that you log P1, and the instructor logs nothing at all. In this case, the instructor is nothing more, legally, than a passenger. If you choose this option, it must be agreed with your instructor in advance, because it has obvious implications on who has the final say if you and your instructor disagree on the correct course of actions (especially, say, in an emergency).
I do definitely agree with Gus' last line - err on the side of caution, and log it as PUT if in any doubt.
FFF
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