Testa was a very powerful captain under Bruno in the 1960s and, it could be argued, he was functioning more as a de facto underboss. Then, when he finally got the number 2 spot officially, he fell out with Bruno over their differing views on LCN (Testa was more prone to violence, he was involved in heroin, etc). From the late-1970s on, Testa was the head of his own faction in the family that was against Bruno.
Caponigro likely didn't kill Testa because, in his mind, he had only received permission to kill Bruno. They weren't on the same side and there did appear to be a struggle in the aftermath (with both going to seperate meetings with the New York families) so that's likely why he wasn't included eituer. And, as we all know, Testa won out in the end.