When you put external AC power to your MH the ATS (Automatic Transfer Switch) is activated. You normally hear a click when that engages Your converter/inverter also has a transfer switch. When 120Vac is provided to the inverter/converter the inverter is usually taken out of service via its internal ATS, but the converter remains connected to the batteries for continious charging as required. Unless your batteries are at the same voltage as the output of the converter, you might see a change in DC voltage for a very slight moment by a slight flicker in your lights. (Batteries serve as a very effective load filter and you may only see a slight ripple on a sensitive instrument or perhaps on an LED bulb.
Your question however relates to only seeing this flicker when connected to a 15A external source. The transfer switches must work the same way on any power source transfer so I am at a bit of a loss as to why this is only noticed when you connected via a higher current rated source, 120Vac should be a constant unless it is not. If you are using smaller gauge wire for the 15A service and the load is 15A, the voltage may not be 120V due to line loss, If this is the case there would be less voltage delta to the converter thus lower voltage to the batteries causing less ripple,
Suggest you take voltage readings under different scenarios to determine if voltages are the same using 30/50 &15A power sources and if you have a clamp on current meter it could provide more useful data,
In addition to basic Volt & Current measurements, I would put my oscilloscope on the DC line but most folks don't have one of these more sophisticated instruments, but simple voltage measurements alone should give you more data than you have right now,
Good luck - I hope I provided useful information.