In Arizona, if the buyer defaults by not making payments and the Notice of Termination is given by
Certified Mail does it then have to go to civil court like an eviction? This contract for deed was
Not recorded.

What are the terms, what happens to the contract when they breech it ? Does it turn into a rental ? What does the contract say you can or have to do

The terms of the contract govern here. Without knowing what the contract says about a breach or default, its hard to answer.

Most such contracts, revert to a rental lease in case of default. If so, you would still need to evict.