The definition of what is "Indian Country" and where the limits of its Constitutionally-ensured sovereignty end is not as cut and dried as "physical borders," particularly when it involves non-tribal members. Thus this bit in the story: 

"The state attorney general's office has no specific policy or guidance on banishments. Generally "banishment orders can present difficult constitutional issues that have to evaluated on a case by case basis," said Cori Mills, an assistant attorney general."

Particularly here in Alaska where, due to the essential lack of treaty-defined reservation lands, the limits of that Sovereignty will often be real but intangible. We are creating and adapting law to fit changing circumstances.

In any event, banishment has a long history as a punishment even in "white" American history, communal beliefs on what punishments are "reasonable" impositions on Rights, and thus Constitutional, and what level of due process may apply, are always open to debate.