Correct. In one episode an FBI agent asks Carmella if Tony knows anything about the Kennedy assasination and she replies Tony was 3 at the time.
So that would have made Tony in the original series born in 1960, and 7 years old during the Newark riots.
Soap operas do this a lot—a child character disappears, and returns a couple of years later as a young adult. They even have a funny acronym for it: SORAS—Soap Opera Rapid Aging Syndrome. In Tony's case, they seem to be subtracting age, a la Benjamin Button.