I think a 10 gallon with a school of tetras is too small, just because they like lots of room to swim and sort of share the same space as bettas (mid to upper tank area). If you could do even 12 or 15 it would probably make a good difference. It also just depends on the temperament of your betta.
I temporarily housed 3 tetras for about 2 weeks in a 10g with my betta and he HAAAATED it. After they were picked up, he came out of hiding. Caught him flaring out his fins at them on multiple occasions.
Tetras need at least a school of 5 to feel secure and happy in a tank, and between them and a betta.. I think 10 gallons may be pushing it, as far as bioload goes. Might be more doable if you had lots of live plants and excellent filtration.
Whether or not your betta will attack them though is.. not easily predictable. Very much down to individual personalities.