Hondas have an additional voltage or load regulator to help in fuel economy.
They call it the ELD, it turns the alt on when battery voltage falls below 12.6 volts. I dont know the upper voltage, but think its near 13.8 to 14 volts. It trys to make the starter battery bare the load of the electrical system vs constantly powering the car by the alt. Theres plenty of stuff online how to disable it.