Anyone who has watched The Sopranos can see that the writers got material from both the New York and New Jersey underworlds. The basic concept of a small, indigenous family in Jersey is obviously based on the DeCavalcantes. A lot of other things were too. The pump and dump stock scam in season 2, John D'Amato obviously being the inspiration for Vito being gay in the later seasons, etc.

And yes, the part about the DeCavalcantes being affiliated with the Gambinos is correct. The same thing happened with what was left of the Trafficante family down in Florida.