Adonis beats "Pretty" Ricky Conlan in the opening scene and then later on in the movie there is a throw away line where Stephen Smith mentions that some people feel Adonis only beat Ricky since he was older and past his prime. This makes perfect sense since in the first Creed movie it was generally regarded that Ricky's match with Creed would be his last match since he was going to prison afterwards and by the time he would get out, he would be too old to really continue his career. Come time we get to Creed 3 and he loses, you could see why make in universe they would make the claim that Ricky might have fared better had he still been in his prime.
The referee during Damian's fight with Felix seems noticeably more strict towards dirty fighting than the other referees shown in the previous films, with him pausing the fight to deduct points from Damian's score and even outright threatening him with disqualification if he doesn't behave. Before Damian got involved, Felix was originally slated to fight Viktor Drago, who rather infamously was disqualified from his debut match after he lost his temper and hit Adonis while the latter was down. While Donnie is on good terms with Viktor now, having a more attentive referee oversee the fight was better safe than sorry.
The only reason Pretty" Ricky Conlan took the fight with Creed in the first movie was because he needed the money to take care of his family since it would be (at least at the time he thought) his last boxing match ever. Since he took the rematch in this movie despite some claiming he was too old, was he taking the match because his family wasn't covered well enough or because he had financial issues?
Conlan is shown to be very prideful and arrogant, which is why - even when taking the first fight for the money - he refused to take Adonis seriously until the latter proved himself a Worthy Opponent. Given his comment during this rematch about wanting to "take back what's [his]", and his cordial response to defeat, Conlan was probably just trying to get the title back for his own ego, and nothing in his personal life was actually at stake over it.
