How do I stay in the same desktop when I switch to a full screen app?
You can't set it to go back to the last Desktop you were in, but you can set it to go to a specific Desktop when you exit full screen.

Just move the application in windowed mode to the desktop you want, right-click the app in the Dock and set to "This Desktop". Whenever you come out of full screen, it will always go into windowed mode in that particular desktop.