Legal advice would be a good thing to get. Except for that recent law on domestic violence on rez I am pretty sure that Tribal regulations apply only to tribal members.

My non-attorney guess is that if a Tribal Officer has the authority through agreements to cite you for a violation of state law, the citation will go to state court.

If they don't have the authority, or may wish to make things "cleaner", they can call in a local PD/sheriff/WDFW and have them do the citing.

About now would be a good time for some lurking WDFW officer or other Peace Officer to weigh in with facts.