MitchDebbie, I have been reading up on this issue. It sounds like it is the type of transfer switch you have (Mechanical relay versus solid state relay) or it could be the generator not putting out enough power.
Your transfer switch is the contact relay type which is susceptible to low voltage condition. Meaning when an air conditioner is starting up and the generator does not put out enough power it can cause those types of transfer switches to chatter.
The only way to tell what is causing you issue is to measure the voltage drop when an air conditioner compressor kicks on.
Sorry I couldn't be any more help. But if you do get your problem fixed please let us know.
2013 Georgetown XL 378
2008 Honda CR-V