Legal Question in Family Law in California

He's not exempt, but a detailed answer is too complicated to present here. You can read about some of the law that County Child Support Service Agencies have to follow here:

http://www.childsup.ca.gov/Portals/0/resources/docs/policy/cssin/2010/cssin10-06.pdf

I'd suggest speaking to a family law attorney familiar with tribal law in California.

He is not exempt at all, but depending on his tribe you may have to obtain your orders in his Tribal Court rather than state court. You would want an attorney who not only knows family and tribal law, but preferably one who has experience with the father's specific tribe.