@TheWhite Hey!
It sounds like you're running into a bit of a controller conflict. In PCSX2 standalone, you can set which controller is primary by going into the Controller (PAD) settings and manually configuring the input devices. If it keeps defaulting to the Dragonrise controller, try disconnecting it or setting the PS4 controller as the main one in the settings.
For PPSSPP, just check the input settings and make sure your PS4 controller is selected correctly as the primary device. If it’s still causing issues, sometimes restarting the emulator after making the changes can help.
Hope that helps! Also, if you're ever in the mood for a fun change, you might want to check out a face switcher tool it's a cool way to switch things up.