Even if you had physically worked in TN, you would still owe IL tax. You report all your income on your resident state return, including the income earned in the other state. Your home state calculates tax on all your income, but gives you a credit, or partial credit, for tax you paid to the other state.
When you worked in a state without an income tax (e.g. TN), there will be no credit, since there was no TN tax. In other words, having worked in a state without an income tax does not get you out of paying state tax on that income, to your home state.
