@hawkeye10,
Can you provide a source to support the claim that tribal courts in the U.S. now have jurisdiction over nonmembers?
Technically, the recognized tribes are sovereign nations and thus it would actually make sense for tribal courts to have jurisdiction over all civil and criminal cases involving matters within their territory. However, their sovereignty has been greatly constrained and diminished by treaties and their incorporation into the United States. An excellent example of this is that they have no jurisdiction at all over nonmembers in criminal cases (see the 1978 U.S. Supreme Court decision in
Oliphant v. Suquamish Indian Tribe) and only very limited jurisdiction in civil cases involving nonmembers (see the 1981 U.S. Supreme Court court decision in
Montana v. United States).
The only way this could change would be a new federal law that expanded their jurisdiction to include cases involving nonmembers or a U.S. Supreme Court decision reversing established precedents holding that tribal courts have no jurisdiction in cases involving nonmembers. As far as I know, that hasn't happened yet and thus tribal courts still have no jurisdiction over nonmembers.