I would think that the reason for pressure spikes due to primer substitution would be caused by going from a primer of lower brisance to one of higher brisance. I cannot fathom it working the other way, but I could certainly be wrong.
I have substituted Cheddite primers for WW or Rem., had the loads tested, and found no pressure increases from the loading manual's stated pressures for the same load with another primer. I believe Cheddites are placed lower on the brisance chart than several others, but I'm going off of memory here. I've got a copy of that chart somewhere out in my loading room.