In this video, Carmine really talks into depth on how he developed his unique grip with the right hand.

Carmine explains that his grip with the right hand was created on accident while playing a Vanilla Fudge gig. It was a very hot day in a small crowded venue, and his sticks started flying out of his hands like mad from all the sweat. He ended up catching one of his sticks at an akward position, using between the first and middle finger as the fulcrum point for that stick. Soon after stumbling accross this grip, he had absolutely no problem get a good grasp of the sticks, and also found that it was easier to twirl the stick to.