The 36-year-old champion appeared to shove his face into Bellew's when the pair squared up for the cameras, and the Liverpool fighter responded in kind.
Bellew admitted to bringing up Stevenson's criminal past in an attempt to rile him ahead of tonight's bout.
"As soon as I said 'pimp' he exploded," the 30-year-old told the Liverpool Echo. "I've got the reaction I wanted. I'm chilled out and relaxed and I'm happy.
"I told him 'you're getting hurt you pimp'. He tried to throw a punch but my team are big and strong dudes. You can't mess with them. All I did was stand my ground. Once he tried to get to me I told him what I thought of him.
"His reaction showed me that he is mentally unstable. He is someone that can't control his emotions. That he is not all there. That is what is going to get him knocked out tomorrow."