According to Scarpa, Mineo became underboss in 1964 at the same time that Colombo became the boss. When the captains were told to poll their soldiers on what they thought, they were asked specifically about having Colombo as boss and Mineo as the underboss. They were both approved and installed at the same time. Mineo was then consistently referred to as the underboss throughout the rest of Colombo's reign and was still the underboss at the time that Colombo was shot.

I don't know where the misinformation about Franzese being the underboss in the 1960s comes from. I know Michael Franzese has said it but I don't know whether he was the original source for that or not. Scarpa was consistent in his description of Mineo as the underboss and he was in a very strong position to know, considering that he (Scarpa) reported direct to Colombo up until he was incapacitated.

Could be something like the Bonanno family in the 1960s when some sources incorrectly identified Galante as underboss when we know from Joe Bonanno, Bill Bonanno and other contemporary sources within the family in the 1960s that Frank Garofalo and then John Morales were the underbosses with no one else in between them.