Riccobene was behind bars for heroin trafficking at the time that Bruno took over and he told the FBI he was surprised at the decision because Bruno had only been a member for a short period of time before becoming boss. Riccobene said that he'd been offered the position of boss in the 1950s and could've been boss instead of Bruno if he wanted it. (Should also be noted I saw an FBI file describe how Pat Massi had been offered the role of boss before Bruno). He later said that Bruno had imposed too many restrictions during his time as boss (likely a reference to narcotics).
As of 1952 Riccobene was a soldier under Gaetano 'Big Tom' Scafidi and when he got out of prison in the 1970s, though it hasn't been confirmed, I strongly suspect that Riccobene was reporting direct to the administration (either to Bruno or Testa). Riccobene was part of a discussion with Testa, Scarfo and Narducci about the death of Joe Rugnetta and who to appoint as consigliere where they complained about the process (specifically how, in the past, every member got a say but now only a select few do). Riccobene's leeway under Bruno likely stemmed from his status as a long-time member. To a much lesser extent that can be observed with Antonio Pollina as well. Pollina lost a great deal of influence following Bruno's rise to boss and complained about being ignored by other members but he was still around. He asked to be made consigliere in 1977 but Bruno politely declined. In 1982 Pollina started verbally abusing Nick Caramandi at Pat Spirito's clubhouse on Bancroft over a loan Caramandi had co-signed on with Mickey Diamond (after Diamond's death, Pollina held Caramandi responsible for repayment). Spirito couldn't intervene because he hadn't been introduced to Pollina as a member so Chickie Ciancaglini had to come down to calm the situation.
There isn't as much on Riccobene's relationship with Testa but we know of his very unfavourable view of Scarfo becoming boss. Riccobene campaigned to get the top spot in the aftermath of Testa's death but failed to gather support from any of the captains.