Direct Page register when using dp addressing modes

This might be a stupid question-- but I am trying to write an 65816 emulator and at the moment I have a few doubts on this: should the direct page register be modified when operating in any sort of direct page addressing mode? Say for instance we have:



The direct page register is something arbitrary like $01 right now... When after forming the indirect address, should the direct page register be modified to be the offset after the operation? Or does it stay the same?

Thanks!

The only instructions that change the D register are TAD=TCD and PLD. Anything else is equivalent to a temporary copy.

Thank you sir!!!