That's just probably how your HU is designed. There are no standards on how an HU should behave when you put the car in reverse with the HU turned off.

For instance, my 2DIN HU has three power states. ON, STANDBY, and OFF. The reverse camera view comes up when I shift to reverse only when the HU is either set to On or Standby. When it's Off, it will not respond to the reverse signal.

The differences are;
On - Normal state. All functions are working (whether it's playing video, audio or displaying the GPS) and sound is coming out of the speakers
Standby - The LCD is turned on and will only show the main menu with "Standby" mode selected. There is no sound coming from the speakers
Off - As it says. The display is dark and the touchscreen doesn't work. You have to press one of the hard buttons to turn it on