Rest assured; your betta is not afraid of the dark. In fact, bettas, like most fish, benefit from a day/night cycle, and he should have a period of darkness every 24 hours. It is fine if that coincides with when you are sleeping and have the lights out in your room. He doesn’t need a special nightlight.
If you have his light on when lights are on in the room, and his light off when lights are off in the room, you should be able to minimize the reflection and therefore the flaring. A little flaring is okay, but you don’t want him to flare too much or it will stress him out.
Fish also behave differently when the lights are out, because of that day/night cycle I mentioned. For example, some fish become more active, and some less active. It may appear to you that he is confused or acting strangely, but he is probably fine.