Being a little delusional can be beneficial as a fighter. Tony scores high on the delusion scale. So, in his mind, he probably thought there was some way he could come back in round 3 and win the fight (which from the outside seems impossible), so tapping would be giving up on his chances. Not tapping to those subs does make him incredibly physically/mentally tough though, but at the same time it's a bit delusional.
Jacare did something like that when he refused to tap to Roger Gracie, who broke his arm, but by not tapping Jacare was still able to win on points:
In Tony's mind he probably had some chance of scoring a finish in some way later in the fight and win like Jacare did.