No, not necessarily, as Georgia is due income tax for the income earned while work was performed in the state. Taxes are due to the state where the income is earned, unless the states have reciprocal agreements for living and working in another state. But since Tennessee does not have income tax, there is not a reciprocal agreement with Georgia. Therefore, taxes are due to Georgia for the income earned there and the amount will depend upon how much income was earned in the state.
Here is information on how to file a non-resident return: