Illinois (like other states) taxes non-residents on income earned from physically working within its borders. Therefore you do have to file a non-resident return in IL in addition to your home state return in MO. MO can tax ALL your income, including your earnings from IL, but you'll be able to take a credit on your MO return for the taxes paid to IL, so you won't be double-taxed.
This FAQ explains how to do a non-resident state return in TurboTax: https://ttlc.intuit.com/questions/1901271-how-do-i-file-a-nonresident-state-return
Note that you should complete the non-resident state return BEFORE you do your home state return.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
