"Many tribal courts cannot afford their own public defender and have only 'advocates' without law degrees to defend the accused."

"The Yaquis wouldn’t have been given the green light from the Justice Department to launch the pilot project without Acosta, a longtime public defender...."

Acosta’s office recently filed motions with the tribal court to dismiss the first three tribal arrests of non-Indian men, arguing that the tribe did not properly implement the new law, including notifying the public of its new jurisdiction over domestic violence cases.

The "new law" is an amendment to the Violence Against Women Act, which you can read here. It seems to have been adopted to pick up the slack for U.S. attorneys who are said to have declined to prosecute too many of the cases arising out of domestic violence by non-tribe members on Indian tribal lands.

From that second link, we see the requirements that the tribal court protect "defendants' rights under federal law," including due process, effective assistance of counsel, "Free, appointed, licensed attorneys for indigent defendants," and "a fair cross-section of the community in jury pools and not systematically exclude non-Indians."