At this high voltage, the gen-set relay board is not getting a shut down command.
This leads to the Kohler Syndrome.. (Que soap opera music)
First, any error codes on the display?
Please verify the out put voltage and HTZ with a DVM at any plug outlet.
If it is really high, read on.
The later Kohler regulators have a strange exciter feedback / regulator system.
A simple bad connect in one of the many mini-spade crimp-connects can make strange regulating issues appear and disappear pending the humidity in the air.
Turn the battery off and open the top of the controller box. Wiggle every mini spade connect and AMP connect on the relay board you can on the regulator and in-line connects. Don't use any spray snake oil products unless needed if you do find a wet or corroded connect that needs it. The relay board gets finicky when it gets wet with some products (WD-40 and others).
If a DVM verifies an out of spec out put after this, then shop for another regulator.
After looking for the controller / regulator $$, you may want to go back and wiggle all again.
There is nothing in the generator/alternator to worry about.
Part Number GM34969