I agree. One thing that I'd like to add is that even a scratch from a cat can be deadly. I work closely with a parrot organization and am currently fostering 2 parrots (1 Amazon & 1 Senegal). I do have a bird room, but, if that isn't an option, keep a spray bottle close by, so if the cat goes near the bird, you can squirt with water. Don't spray in the face, but this is a humane way to teach the cat that the bird is off limits, because you aren't physically doing anything, so you're not a suspect in where the water came from.
The only problem with this is what to do when no one is home. That is where it's better to make sure that either the bird or cat is in a separate room if no one can supervise. Good luck!