Hello. This sounds like a calici virus, which can cause ulcers in the mouth that lead to excessive drooling and foul breath. If you can look in there mouths, do you see any red spots on their gums, tongue or roof of their mouth?
Thanks. Was the male still showing signs of the excessive drooling when the vet checked him, or had it resolved?
I would attribute the eye issues to a mild viral conjunctivitis. One of the primary causes of conjunctivitis with excessive drooling in cats is calici virus. It seems to fit all criteria in this case: drooling, irritated eyes, transmissible from cat to cat, resolves quickly. Calici virus is one of the respiratory viruses that commonly affects kitties (the others being feline herpes virus and the bacterium chlamydia psittacci). Calici is unique in that it also causes ulcers of varying degrees from the tongue to the pharynx. These lesions tend to heal quickly, and I suspect had healed by the time the male was examined. Check the others carefully, and you may find evidence of some oral ulceration. Although, sometimes the virus will only cause microscopic lesions, just enough to cause oral pain and salivation.
Other possible causes of excessive drooling could be toxin exposure, liver disease, nausea, etc. These would not follow the course of the disease you are describing however.
The course of the disease points towards viral infection and all of the symptoms point towards calici virus. As you are seeing, this condition usually passes quickly. Reasons to initiate a vet visit include:
1) Not eating for more than one day
2) Acting severely ill or non-responsive
Other symptoms you may or may not see are:
4) ulcers on the pads of the feet
These signs will vary depending on strain of the virus.
Treatment is supportive care. Antibiotics are sometimes indicated, if a secondary bacterial infection develops, but these will not affect the course of the viral infection.