I thought Cicci was in Tessio's crew. We see a hint in the scene where Sonny embraces Michael before he meets with Sol and Mac. Look in the background and you'll see Tessio going back and forth, and then gesturing to Cicci to come with him. Also, it seemed to me that "excuse me Sal" at the end may have been another hint.
Cicci was orginally part of Sonny's regime. When Sonny visits Lucy's apartment, you see Cicci as one of his bodyguards. I think he was later transfered to Clemenza's regime, which is how he became Pentangeli's right-hand man.
