Here is the Wyoming Supreme Court’s decision in Coyler v. State Dept. of Transportation. This case contains a very nice review of the various state and federal cases involving the authority of tribal cops to detain non-Indians until state law enforcement arrives. An excerpt:

Viewing the facts of the instant case in the context of the law just recited, we must conclude that nothing occurred in the detention of the appellant to render his arrest unlawful. The appellant could not have been arrested and prosecuted within the tribal court system because he was not a tribal member. He could not have been arrested by the B.I.A. officer and prosecuted within the federal system because the DWUI offense was a State offense, making him subject to arrest and prosecution by the State. Despite the jurisdictional olio on the reservation, the law is clear that the appropriate action to be taken in circumstances such as those presented in this case is for the reservation officer to detain the appellant for formal arrest by a state officer. That is what happened.