Yes, both states are allowed to tax your income. Alabama may tax the income you earn working in Alabama, whereas your resident state (Georgia) is allowed to tax all of your income. To reduce the effect of this double-taxation, your resident state will give you a credit for the taxes you pay to your non-resident state.
You will want to make sure that this credit is being calculated on your Georgia return. It is recommended to prepare your nonresident return first, so that the credit for taxes paid to Alabama may transfer over to the Georgia return. However, if you did not do this, then review the Credit for taxes paid to another state section of the Georgia return. To calculate the credit, enter in the amount of income you earned in Alabama, then the tax liability for Alabama. The tax liability is the amount of Alabama tax withheld minus Alabama refund, or in addition to Alabama tax due. If what you saw owed to Georgia was a particularly large amount, these steps should lower it (and perhaps eliminate it).
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