I think most of us prefer to take the safer than sorry approach, unless our birds actually do get along.
It was never my intention to allow my first cockatiel and cherry headed conure (got within a little over a month of each other, tiel young, conure older) to become cage-mates, but Casey (tiel) kind of grew on Noel (conure). Noel never meant any harm, but he would lash out at first at Casey. As time went on, Casey became close enough to Noel that Noel accepted preening from Casey, they would sleep cuddled up together on a perch, and Casey could eat food that Noel was holding in his foot.
Charlie, my mitred conure (similar to cherry heads) got along with a lilac crowned amazon in his foster home but tried to bully a blind ruby macaw in the same place. Although he can't cause any damage to me (a result of his attack on the macaw, missing half of his lower beak), he could still hurt one of my smaller birds, so I don't trust him with the little ones. All the small birds (4 cockatiels and a bourke) all live together in one large flight cage.
It sounds like the greys were not happy about Nema being on their cage because it's their area. They may continue getting along away from the cages, just not at the cages. If they don't get along, you may need to train them to station (stay put) and ignore each other.
Do the work it out like cats? Scream a bit, maybe swing a couple of times then get over it?
I'll be honest, and say I wish my cats fought like that!

If my two cats see another cat, they'll get into a fight with each other! And it's a full throttle, claws out, fangs showing cat fight. They'll be kicking, hissing and screaming at each other! It's just a full out fight. As long as they don't see another cat, they do occasionally get into fights, but it's more sibling fight than a battle.
Lucky me, my sister and her family, including two cats, moved in with me a week ago! My cats *DO NOT* like my nephew (two in January) nor are they happy about the presence of other cats! So with them, if two cats are out, the other two are locked up in a room, and they take turns coming out! Thankfully, the cats aren't interested in each other enough to instigate a fight, but my cats are not happy about being unable to enter the master bedroom that one of them used to sleep in... because that's the room my sister has been given.
If your birds end up not liking each other, you may have to do the same and only allow them out at separate times.