The acceleration of the cat shot (0 to 140 kts - 260km/h in 3 seconds) causes your inner ear to make you "feel" like you have pitched down when the acceleration of the cat shot ends. You "feel" like you are pointed nose down at the water (not "inverted" as you mention in your question). You must ignore this "feel" and fly instruments only. Your "feel" would have you yank the stick back, at very slow airspeed and very low altitude, cuasing you to stall and hammer-head into the water (it's happened several times in the past).
A night cat shot is a pure instrument scan where you ingnore your "feel" and rely totally on instruments. For a night cat shot, you put your survival flashlight on your back-up gyro (in case of a gen failure), you set a safe single engine climb attitude (just in case), and you PRAY nothing goes wrong with the jet.
I would argue that a night cat shot is a true 0/0 takeoff (black sky, black water, no horizon, no terrain, no references other than instruments).