It's possible that the difference is the processing the iPhone is doing to its own photos rather than the display settings. It might also be possible that the iPhone is adding data to its own photos that are then interpreted by the HDR display setting and imported photos don't have these hints.
One way to test this is to view both photos on the computer.
If you want to move all PSD files to other directory follow the next procedure:
Goto Library, Filter
In text select Filename, Ends With, write psd
Ctrl+A (or was Option+A on Mac) to select all the files (psd)
From the left panel navigate to the parent directory where you want to create new directory or directly move files to existing one.
In case of ...