The moon cycle simulation on the AquaController follows the true lunar cycle. So like the actual moon, it may be up (moon light on) during the day. Typically, new moons rise in the morning and set in the evening. The moon rises about 50 minutes later each day, and by the time it is a full moon, it is rising in the evening and setting in the morning.
If you want a night light simply program a light to turn on when the last light turns off, and off when the main lights go on.
Curt