Is he eating? And they are either going after him or he is sick. It looks like fin rot though... Do you have a carbon filter? Meds?
All of my bettas I had (well, gave 9 to the LFS(private) tank and all, so one now) had fin rot when rescued from Petco. I just demanded them for free as they were in cups with other Betta fish.
The base of the tail turned silver and rotted upwards. I gave them meds and they all lived and regrew fins.
That water is too alkaline for any barb, I think. May be causing stress, leading to immune deficiency.
I suggest watching him. If tommorow morning his tail is missing fin, and you don't have meds, and he isn't eating and is simply suffering....
Euthanize. It pains me to say it, but for his sake and the tank's sake.