Hi, I had the same or at least a similar problem.
First, you could check if it's the same parameter (Osc pitch) that is affected with other presets as well. For me, it changed with presets, but always something was altered (and always by the same amount) when hitting Start/Stop.
Well it turns out that this is some Midi information that is sent by the DAW which is related to changing presets. If your Midi track or plugin has some parameters called "bank" or "patch", for example, you can try turning them off. If not, this is what works for me:
Set the bank and patch parameters MANUALLY and watch the Prophet's display, it should scroll through preset numbers. Do that until you find your desired preset and leave it there. When pressing Start or Stop everything should work ok now.
The only thing that still happens for me is that every time I start playback, whatever I have edited is lost as the last saved state of the preset is loaded again. So save in between Starts and Stops. At least until you can figure out how to filter out these subliminal Midi messages.