Cage dominance is one of those phrases I absolutely hate, because it usually isn't even close to what is happening.
What you had was a bird that was afraid to step up, and trying to get you to back off so he/she wouldn't have to.
Now that the bird has learned that this isn't anything to be afraid of, and, oh by the way, I'm gonna make you do it anyway bird, whether you bite me or not....
THE BIRD ACCEPTS IT.
I believe that is the true dynamic in this scenario.
You can get birds who become cage territorial when they've been locked up too long, and that is more a "defend the nest because it's all I have left" situation. If I lose my home there's nothing left for me. That's where the food and water is. That's where my toys are. That's my safety and security...
That's the dynamic that happens when birds get cage bound. Convincing them that YOU AREN'T taking their home away from them is how you reduce those behaviors. And the first few times, you may need to struggle with it.
THE BEHAVIOR DOESN'T IMPROVE UNTIL THE BIRD "GET'S IT." Once the bird figures out that he still has a home to go back to,and everything will be where it always was, PLUS I get interaction and fun, and new experiences outside the cage, it's no longer a problem.
Cage dominance, like height dominance is a myth in my opinion. That isn't the dynamic at all.
Locked in a cage, they're backed into a corner already. ALL animals have a fight or flight instinct. (The flight instinct in birds is usually the stronger of the two, unless it's an amazon, or a sennie, or a macaw that has become territorial.) Since they're locked in a cage and there's nowhere to go, FIGHT instinct takes over. When you're not considered a threat, the fight or flight reaction no longer occurs. THEREFORE, the bad behavior stops.
TRUST is the correct answer here... YOUR BIRD IS LEARNING YOU ARE NOT A THREAT AND IS STARTING TO TRUST.
Does that make sense?!