Yes, you need to keep your controller powered on to run the program since our lights do not retain any programming. The controller sends commands to the lights at scheduled times.
If you are concerned about the light that the controller screen emits; as long as you are on the home screen, your screen will only emit a green light which has no effect on your plants during the dark period.
You can power off your controller if you do not wish to run any program or keep your lights off. You can also use the controller's manual mode to simply send a specific spectrum to your lights and then shut the controller off. This will cause your lights to remain powered on with that spectrum indefinitely, or on a schedule if your lights are plugged into an external timer.
As long as you keep your light switched to controller mode, it will remember that last spectrum every time it powers back on or until you change it again with the controller.