I have 2 small dogs who think the furniture in the house is there for them so they are always on it. I also have 3 cats, (2 are indoor) one of the cats is totally blind. MY cats never bother the birds, they are too big for them, but occasionally my outdoor cat will stalk my parakeets in their cage, but gets a stern no and a spritz from a spray bottle. It rarely happens anymore. All my animals are afraid of the birds, Nilah my amazon will run towards any of them and bite them, and they run the other direction.
In the beginning though, I never took my eyes off of any of them until they felt comfortable and I understood their behaviors and acceptance of each other. Tragedy can strike in a second, so never allow them out unsupervised in the same room.