This is sort of correct, from my understanding chatting with Shane and Mike from Genesis yes you do need to see above 13.1 but this is sort of misleading.If you have the genesis dual battery system you will want your charging system to stay above the 13.1V threshold so that the 2nd battery charges while running. Just an FYI I also have the genesis dual battery system with a fridge full time etc. I found that by simply disconnecting the IBS sensor on the battery ground cable my alternator voltage is constant 14V+. Might want to go that route if the 2nd battery is not charging sufficiently for you.
On startup the Genesis system looks at voltage on the main crank battery and upon starting once it sees 13.1 for several minutes it closes the solenoid and connects the two batteries together and charges as one and from my understanding this reduces the load on the alternator so if your JL Sits say for several days and the voltage slowly drops to 12.7 +/- .1 the Cole Hersee solenoid opens and separates the two batteries to protect the main crank from getting lower if you are pulling off the aux but it does not keep if from getting lower due to parasitic draw from what comes off the PDC.
Once you start your JL the alternator first starts charging the main since the batteries are disconnected if the main is below the threshold and after several minutes of seeing it above 13.2 it closes the relay and connects the two batteries and they are treated as one big battery.
I have been testing the Genesis system for a few weeks and the batteries are connected as one over 99% of the time it’s only when your main falls below the 12.7 threshold that they separate and then it’s only for a few minutes.