Mitchell,
It does not sound like this man owns or rents any property there so he must be on someone else's property, trespassing. 
You are correct that Alaska, with the exception of Metlakatla Indian Community, located on the only federally recognized reservation in Alaska, the tribes only have authority over their citizens (members). Few people know that Alaska is a Public Law 280 state. However, should the state ever want to give up that status, then the tribes would not be subject to State laws, if their land can be considered " Indian Country". They would however, be subject to Tribal law and to Federal law. 
At the time Alaska was "made" a PL. 280 state, no one, certainly not the Natives were given a choice or say about it. 
But, if you live out in the isolated villages where weather can determine how long it take a Trooper to arrrive, then you might better understand that the tribal government is Law there because no one else is. 
The man needs to leave. He is not wanted there.