Always an interesting thing to observe. My birds are all relatively mellow, except for Coco, who will try to bite every bird except for Joey. He and Joey get along fine. Joey gets along with all the other birds. Cricket and Stickley get along well with each other -- they go into each other's cages to visit. Sometimes Cricket preens Stickley.
You are right -- birds who had bonded with their owner do get jealous of other birds, so each bird gets handled separately, to avoid problems.
Based on all my years of reading stuff from bird owners, it would seem that most birds bond closely with one person, which sometimes makes it difficult for other people in the household. Birds sometimes decide that they thoroughly dislike a person, and will try to attack that person whenever they can. People sometimes give up a bird for adoption if it is creating too much havoc in their relationship with another person. Or people will give up a person if it is creating too many problems with a bird.
Every household is different, of course. I've heard stories that go from one extreme to the other -- all the birds get along really well to none of the birds gets along with any of the other birds.
When adding a new bird to the flock, it's always best not to assume that it will get along with other birds. If it does that's great, but there is no guarantee.
Coco used to get along with other birds, but suddenly he didn't and two of my birds wound up going to the vet for emergency care as a result.