I recently got a new kitten. My birds were used to a cat, but the cat was here before them, so the birds were very cautious and leary about him. Sadly.....the coyotes here got my cat.......
When I brought the new kitten home, Talon set out to let that kittne know first hand, that SHE was the boss, this was HER house. She spent the first day or 2 chasing the cat around the house(she is fully flighted), dive bombing the poor kitty, and screaming at it as she did so. Rikki on the other hand, just tries to bite him as he walks by. The kitten knows who is the boss in this house, and never goes after the birds, but that doesn't keep me from keeping a diligent eye on them all....just in case.
I am sure you will be fine, and I am very happy for you! My advice to you, is NEVER trust that those CAT instincts won't kick in when you least expect it.