Am confused about this myself. Say if you're a holder of Japan passport and also US passport and you are coming back to Japan. Since Japan doesn't accept dual citizenship (with few exceptions), wouldn't the Japan customs be curious why you only have the Japan check-ins and check-outs of the country and nothing else? Would you be detained or something else?
If Japan doesn't accept dual citizenship how can you have two passports?
My experience has been that you simply need to present your destination passport, leaving the other one in your bag. When I last went to the US I presented my US passport in Auckland (upon leaving) and in LA (upon arrival), and on the way back I presented my Australian passport at San Francisco (as a naturalised Australian I am allowed permanent residence here).