Hi Joann,
Generally birds that are not in the same cage will not form a close bond, as far as to the point that they won’t let you handle them. But, you didn’t mention what species they are and if they have ever been tame. A new bird should not be in contact with any birds you already have for safety reasons. They certainly should not be having physical contact such as beak to beak. Birds can be sick when you buy them but not look sick. So it’s always best to keep a new bird in a separate room for 30 days. Since they have already had contact, it’s too late to quarantine the new bird, but you should move the cages further apart and watch both birds for any signs of illness. When birds can have contact between cages, they tend to bond more, so you should keep a few feet between the birds so they focus on you and not each other for taming and training.
Thank you for asking Lafeber,
Brenda