You're making me want to set up a tank again lol. I had beautiful one with black neons lemon neons a few rasbora and a pair of blue rams. Definitely one of my all time favorite setups.
I've seen some of the male tetra pick on the other tetra quite aggressively for sure. Pretty sure the males can get aggressive when they're breeding. Not 100% but I think that's what was happening at least with mine. I never seen them breed but there were babies now and then in the plants and drift wood.