The word "commonwealth" doesn't mean a thing in terms of customs and immigration. Also, a commonwealth is a territory, but not all territories are commonwealths. The two US commonwealths, PR and MP, are commonwealths because they created a document approved by both their peoples and Congress. The rest of the territories operate on organic acts which are US law changeable only by Congress.

In PR's case, they are included in US customs and immigration jurisdictions, but in MP's case it's completely opposite. GU, AS, and VI all have their own customs, and while AS has its own immigration jurisdiction, GU and VI fall under US immigration jurisdiction.

And even under US immigration jurisdiction, there is immigration pre-clearance from GU to HI but not from HI to GU because GU has more relaxed tourist visa policies.