In the shootout that follows Pentangeli's strangulation, Cicci is grievously wounded and is left lying in the street as everyone drives away.
I always assumed that he was also presumed dead and holed up with Frankie until the hearing.
At the least, he was surely arested and charged with serious crimes, so I can't imagine he was promoted to a more powerful role.
In the spirit of speculating based on known movie characters, here's a theory for you: Michael had Don Altobello manage things in NYC until he stepped aside for Joey Zasa.
That has been a strong theory for a number of years. Don Altobello came out of left field in the movie, yet was Connie's Godfather, connected to Zasa, and had connections to Sicily.
