It seems that she's afraid of you. Tiels usually behave in that manner if they feel threatened. If she's a tame bird and has been handled all her life, she shouldn't be that way. In that case, you'll have to work on taming her...and that would require letting them out everyday.

She could very possibly be screaming because she wants to come out. I know my birds would literally go insane if I locked them in a cage, and though they are very quiet birds, they *would* scream, for sure, if I had them locked. They scream every morning when we take their cover off to make sure we open their door. Once its open, they settle down. I know I would go insane if I wasn't allowed out of my room. Tiels feel the same way.

Do you think you could lock the cats out of their room for an hour or so everyday to let them out and play? That would give them the freedom they want for at least awhile, and you'll be able to bond with them too. I don't think its possible, from my experience, to bond and become friends with a bird that can't come out of their cage.