This is an engineering question, and there's computer hardware and software logic designed specifically for "If/when do X/Y." I've written code for systems that do far more complicated things than having 2 power sources for 1 set of controls.
Beyond the scope of this thread, but it's not only technically possible, it's technically easy to have the controls capable of running by either battery or grid power, and it's pathetically bad design architecture to have it working this way.
Either way, I see that's not how this system works and will adjust my settings to work around it.
Thanks
@timselectric for your help!