Almost correct. If you are not a member and your victim is not a member, tribal police can detain you until the local LE has been notified and arrests you. You will face state criminal charges. If either you or your victim are members, tribal police can detain you until a BIA officer or the FBI is available to arrest you. You will face federal criminal charges. If both you and your victim are members, then tribal police will arrest you and you will face a tribal court (depending upon the tribal structure a tribal court is a federal court), if one is available else a federal court (Oliphant v. Suquamish Indian Tribe, 435 U.S. 191 (1978)).