Carlo went from being kept out of the family business, to fully participating in the high-level Capos meeting when Michael takes over the family business, "pushes" Tom out and says Carlo will be "my man in Vegas." This latter closeness turned out to be part of a Don Vito/Michael charade to make Carlo feel comfortable.

1 - Were Tessio, Clemenza and Hagen part of the charade as well? I don't think so. Hence, they were pretty stupid to speak so candidly in front of Carlo, who was always suspected of having a hand in Sonny's killing. Weren't Tessio, Clemenza and Hagen suspicious? Carlo might have even tipped off Barzini that defiant Tessio was ready to become turncoat.


2 - Was it not very very risk to let Carlo live for so long and even promote him? It took about 4-5 years from 1951 to 1955 to knock off Carlo, who could now easily be blackmailed by Barzini into doing anything to harm the Corleones. Carlo was not part of Don Vito's promise to not break the peace (i.e. like Paulie).

Regardless of Tessio's, Clemenza's, and Hagen's presumed suspicions, it was Vito & Michael running the show and they let Carlo think what they wanted him to think. Carlo was most likely too dumb & self centered to percieve Tessio's unhappiness as a prelude to becoming 'turncoat'. Once annointed with the 'man in Vegas' position, they knew he'd be a happy camper and have nothing to do with Barzini.

Apparently not, since once he fingered Sonny for Barzini Carlo was apparently a loyal Corleone from then on. It wasn't too long after Santino's death that Vito was able to bring Michael home, and begin grooming him to run the business. Peace and a narcotics deal having been made, Barzini would probably know to keep away from Carlo, who had basically already served his purpose.

I would not have pictured the Carlo/Barzini collaboration as a long term one.

Apple

Exactly, Apple! Unlike Paulie Gatto, who was greedy and committed his treason for money, Carlo was out to settle a personal score with Sonny for a) not letting him get a big piece of the family action; and b) the humiliating beating Sonny inflicted on him. Once Sonny was dead, both Carlo and Barzini had gotten what they wanted.
Of course Michael and Vito knew better, and no doubt were careful not to discuss anything too dangerous to them in front of Carlo. But even if they assumed that Carlo was still spying for Barzini, it'd be in Michael's interest for Carlo to go back to Barzini and tell him that Michael was seemingly reluctant to act against Barzini's transgressions on Tessio's territory, and that Tessio and Clemenza seemed unhappy with Michael's apparent weakness in the face of Barzini's provocations. That info would have made Barzini underestimate Michael, and show his hand by setting up a meeting through Tessio.