Not exactly or at least not all of them. NRT(Narita) is the opposite for example. It's International terminal is far busier than the attached domestic terminal at T1 there. For both T1 and T2 @ KIX(Kansai), their international section is just as busy as the domestic section. For most other japanese airports, domestic terminal being far more busy than international terminal makes perfect sense. Their quantity of domestic flight and passenger outnumber international ones typically by a factor of at least 10 : 1 on a daily basis.
There's another onsen(hotspring) also inside the terminal @ NGO(Nagoya Chubu). I have not tried it and used my time at NGO to visit its aviation museum instead...a very interesting place including an original Boeing 787 prototype inside.