All your income is taxable by your home state of GA, regardless of where you earn it. Therefore your employer is correct to withhold GA taxes.
As long as you do not physically work within Illinois, your income is not taxable by IL, even though your employer may be located there. Some states tax non-resident remote workers, but Illinois is not one of them.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
