Some people do seem to have luck with things they shouldn't do (my best friend has a tank with mixed temperaments too, and everything is fine). The betta's fin will not regenerate, but as long as it has stopped, he should be ok. If you notice fins being nipped you can keep him in a breeding box until you can get another tank cycled long enough. Be sure to keep the water clean (biweekly water changes 20% of the water) while his wounds are healing... he'll be especially susceptible with an open wound.

Good luck.