To elaborate on @Anonymous_ 's answer:
Any income earned from work performed in Georgia is taxable by Georgia.
ALL your income, including your income from GA, is taxable by your home state of AZ.
You may claim a credit on your AZ tax return for the taxes paid to GA, so you won't be double-taxed. But you must file in both states.
In TurboTax, be sure to complete the non-resident state return before the home state return, so that the program can correctly calculate and apply the credit.