I've had a male betta with a school of neons in a 10 gallon and they did fine together. When I first got the neons,they would stay at the bottom huddled together near a cave and plants. Placing floading plants will definitely help them to feel more secure and subdue the brightness for them. I honestly don't think it's the betta that's freaking them out. The betta probably couldn't care less about them. My neons were so bold with my betta that they actually stole food right from his mouth (bettas are much slower).
The other thing I noticed when I first got them, that they did swim around much more when I shut the light off. It appeared that they felt more comfortable swimming around and exploring their new home in the dark (room lit tank).
When I upgraded to they 27 cube, they did the same thing. They have been in that tank for over a month and they just started swimming to the top to get food the last week or two.... They do seem to prefer the lower half of the tank.
I'm not sure how long you've had your neons, but it will take them some time to get comfortable. Once they do, they will put on a show with their chasing, bickering, and schooling all over the tank. My hatchets took even longer to feel secure in my tank and it's very heavily planted.
