How does a charger with a single output charge two batteries: house and engine? How does it know when the engine battery is full-up and when to focus on the house bank? How does the alternator/regulator work to charge the two batteries?
The charger charges the house and the ACR allows the engine battery to get a charge whenever the house is being charged. Without delving into battery chemistry, voltage, and associated resistance, simply put, either battery will receive the charge it needs based on its own level of discharge. A full starter battery will receive very little amps even though it experiences the exact same voltage from the depleted house bank. It's not rare to see a house bank getting 95 amps and the engine bank getting 1 amp. Battery charging is not a sequential thing: it's not house bank and then engine bank. They both get a charge whenever the charging voltage triggers the ACR. The charger and alternator follow the same charging characteristics. The only difference is the source of power: AC power for the charger, or engine power for the alternator.