i didnt think blackskirts were that aggressive, havent seen it before, and they are very small right now. maybe by the time they grow out they will be used to him. but i will keep an eye on it.
Hopefully the blackskirts (and serpaes) will stick to their own schools...a lot of people haven't noticed any nipping from either fish but as a precaution I would definitely keep an eye out for any fin loss and remove the betta immediately. Adding to both tetra schools will also help them stay within their own pecking order.