If Cali was actually arrested and booked, there would be a paper trail and someone would be able to find a record of the arrest. Someone who can access those records should start digging. Also, as someone else mentioned, just because the police came out doesnt mean he was actually arrested.

Next, as to John Gambino speculation, just becuase he's got the power doesnt mean he's the actual boss. Gamino could still be a very powerful captain and have named Cali as the actual boss, but if Cali pissed off the rest of the Sicilian faction, then Gambino mightve turned on him. Cali then couldve lost some of his power base. Like, Cali's power as boss came from Gambino's crew and all of the Sicilians. If he loses even a chunk of that then that would erode his support as the boss.