We have a 2017 Host Everest and seen similar problems. Not sure what is causing it yet. Note, you will find another GFI outlet in the bath area. The one thing I have noticed is that after the generator starts there is a time delay of up to 15 seconds for the microwave to fire up. This is first TC I have had that has an Automatic Transfer Switch. I haven't crawled into the basement to find out exactly the system works.
Our only other ATS experience has been in an older Foretravel MH, the high end stuff and there the ATS switched immediately. I'm not too sure about the quality of the electronics Host uses. The WFCO converter that came with it did not charge batteries properly so it got changed to a PDI.
In other TC's I just used a jumper and plugged the generator into the 120 input. Going on first extended trip in 2 weeks so will find out more. We'll be back near Columbia MO in early May if Your want to get together(send PM). Heading to Arkansas in a week or two to find spring and escape from mud/snow season in the Rockies.