Cats can never be trained to be trusted around small furred or feathered friends. They can learn to be sneaky and wait until your back is turned, but never actually 'safe'.
With smaller birds the main issue is that the cat will go for the bird through the cage then tip it over, releasing the cage/base catches and/or scaring or hurting the bird in the fall.
I am currently looking after my sisters degu's while she is away training- I have their cage secured to the wall (well, fireplace, but close enough) to prevent it bring pulled over and have a lock on my living room door to stop the cats getting in while I'm not there. My big Mac and amazons look after themselves if the cats show an interest, and the door lock is to preserve the cat, not the birds!
Why can they not be in the same room as your rodents? I currently have 3 gerbils, 2 degus, 1 macaw and 2 amazons all sharing a room. My Mac is totally fascinated by the gerbils and degus and just loves watching them

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