A continuous leak from the horizontal "cap" on the upper supply is typically a symptom of insufficient water pressure or an obstruction in the inlet filter screen in the threaded shank your water supply line is connected to.
These two factors could also cause the vertical "cap" to leak but debris build up on or degradation of the rubber valve under the vertical "cap" could also be the cause.
In the first scenario, the water doesn't enter the system with enough force to close the vacuum breaker (horizontal cap) and in the second scenario the air inducer valve (vertical cap) that draws in the necessary volume of air as the water flows past it is either not fully opening to allow sufficient air draw or not fully closing to retain the air.
Based on the serial number on your Flushmate and a little Q&A, the tech who returns your call should be able to help you identify the actual cause and assist with a resolution.
In the meantime, I hope this info is helpful.