You can never COMPLETELY trust the cats/dogs around your smaller critters, but when I got my last kitten, I purposely let the birds show him who's boss!

They would nip at his tail and ears and he learned right quick that those feather things BITE!! lol I do not EVER trust him (or BK) alone with the fids out, but both the cats know the 'evil eye' mom gives them along with the sharp NO! when they get that look in their eye.
I have a video of one of my tiels chasing the cats, and it is hilarious, but I AM RIGHT THERE obviously. When I leave the house, the fids are put in their cages.
I raised my cats with the birds so they know they can't touch them, but instinct is instinct and cats will be cats. NEVER LEAVE THEM ALONE together.