For some purposes yes, for others no. The state has jurisdiction in matters not involving the tribe that take place there and the residents can vote / participate in civil government as Arizonians. However, the nation does have sovereignty in tribal affairs on the reservation and a few outside it.
[1] “Daylight Savings Time explained”, CGP Gray. https://youtu.be/84aWtseb2-4. Skip to the 5 minute mark for Arizona.