Treat instinct as the starting assumption
A dog that has lived gently beside a cage for years and a cat that ignores the budgerigar all morning can still react in a split second to a flutter, a fall, or a sudden flight across the room. Birds are prey animals, and the safest indoor system starts from that fact rather than from how trustworthy your other pets usually seem. A playful swipe, a pounce meant as a game, or even a dog's mouth closing in excitement can break fragile bones or cause injuries that are not survivable for a small bird.
Saliva from cats and dogs also carries bacteria that can make a bird seriously ill after even a minor puncture, so any contact that breaks skin, however small the wound looks, means prompt avian vet advice, not home watching.
Separate spaces, not just supervision
Build safety into rooms and doors instead of relying on someone watching every second. When the dog or cat is loose in a room, the bird is either in a secure cage with a latch that paws cannot lift, positioned where it cannot be knocked, or in a different room with the door closed. Check cage bar spacing and door catches, because a determined cat can reach through wide bars and a clever parrot can open a simple catch from inside.
Out-of-cage time gets its own rule: bird out means other pets out of that room, door shut, and one named person present for the whole session. Never leave a bird loose and unattended while you answer the door, and never let a bird ride on a shoulder into a room until you know which animals are already in there.
Introductions, if they happen at all, stay at a distance
Some households let a cat or dog see the bird through a closed glass door or from across a room while the bird is securely caged, purely so the novelty fades. Keep those viewings short, reward calm behaviour in the other pet, and end them if either animal shows fixation, stalking, barking, or stress in the bird such as crouching, alarm calls, or trying to move as far from the other pet as the cage allows.
Never hold the bird in your hands near a dog or cat to show them to each other, and never let another pet sniff a bird at beak level. Distance and a barrier are the whole method; closeness adds risk and teaches the bird nothing useful.
Give every household member a job in the system
Most indoor accidents follow a simple gap: one person let the bird out while another let the dog in. Prevent that with a shared rule everyone can state, a closed-door habit, and a quick check called out before cages open.
Rotate responsibility for the final evening check as well: cage latched, water changed, other pets settled in their own spaces, and the bird's room door pulled to. That last walk-through, done by a named person rather than whoever happens to pass, closes the gaps that daytime rules leave open.
Assigning those room checks and out-of-cage sessions through KinsLe's Care Teams means each duty for your bird is given to a named family member or helper, and completed tasks are marked with a timestamp so nothing is assumed.