I did some tinkering and just found out this:
Vampire invasions will happen with a servo in the household as long as the servo and every other household member is asleep in bed. You have to click recharge on a bed and not the servo itself.
But then I'm running into another issue: the servo with the defence module turned on would not autonomously zap the invader. It wouldn't even zap when I tell them to.
Is that fixable? Could this be caused by the mod?