Where federal and state jurisdictions overlap, both jurisdictions may charge you with the crime. You may wish to hire a civilian lawyer to represent you for the DUI or to make sure the local jurisdiction knows you are being prosecuted as a member of the Armed Forces.
Hopefully the prosecutor would defer to the military proceeding and not double charge you. Even if you are not charged as a military member, the outcome of your Arizona DUI could have an effect on your military service. If you can’t afford an attorney, one will be appointed to represent you.