No, there is no link that I remember between the heart and the generator. Now some of the newer zantrex and prosines will auto start the generator but I've only seen that on the hi-end MH, the big buck ones. Check to make sure you don't have the heart turned on by mistake, in the invert mode. This will cause the inverter to run all the time, whether you have shore pwr or geni pwr. An easy check is if you have no shore or geni pwer and the tv/mw etc is working, the the inverter is in the invert mode and your running off of the batteries. The batteries will only discharge down to 10.5 volts and then the inverter will shut down till the batteries are charged back again. Hope this helps.
Renegade (Jim) & Wrangler (Doreen)
& 4 attack cats, TJ, Shadow, Chessie, RJ
along with 2 who adopted us, Tom & puddy.