Tribe Law, Agency
While tribal police, as a class, are considered federal employees as a matter of law, as they are enforcing order pursuant to a contract with the BIA, the question of whether any person is acting as a tribal officer is a question of fact to be resolved at trial.
http://media.ca8.uscourts.gov/opndir/16/01/143888P.pdf
Since 2011. An occasional commonplacing of the U.S. Circuit Courts of Appeal.
Neither an authoritative statement of the law nor legal advice. Quick work.