The game was designed for xbox 360/xb one controllers, 'cause they're actually a totally official controllers for all modern pc games. Sometimes game developers adds DS4 controller support too, but not so offently.
It seems like the game won't support Dual Shock 4 so good as x360/xbone controller. That's so much for most pc games. In the game's launcher there's manual controls mapping. Have you tried to remap properly?
About camera spinning. I guess, one of the axis for camera movement is mapped like (AXIS Z- "left analog stick - left") and the ps4 left trigger is (axiz z- = trigger at default possition, axiz z+ =trigger pressing). That's why the game thinks you pressing analog, when you actually didn't do anything.
P.S. Butterflies' confirm button is 'A' on Xbox controller by default.