I have the same generator and it does the same thing. When I connected it to my 5r and turned on the 15K AC my voltage meter inside the rv fluctuated like a pulse, varying the voltage. I called Champion and talked to a tech which informed me that the generator is working properly and not to worry.
My son in law works for prevost and he said the term is the generator is hunting. He also didnt think it was anything serious to be concerned with.
I bought this as just a cheap emergency generator, and even though I've ran it a few hrs at a time as to test, I am concerned with using it long term. I am impressed with how quiet it is for the type of generator, and it starts very easy, but like you I'm nervous about using it.
There customer service is readily available so you might give them a call and see if you get the same answers as I did. I'd sure be interested in hearing back from you.