Your earnings for serving in the Armed Forces Reserves are NOT taxed by Illinois.
But your earnings from working as a civilian in Illinois ARE taxable by Illinois.
Therefore you must file a non-resident Illinois return, in addition to your home state Missouri return.
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.
In TT, be sure to complete the non-resident IL return before you do your MO return, so that the credit can be calculated and applied correctly.
https://www2.illinois.gov/rev/questionsandanswers/Pages/100.aspx
**Answers are correct to the best of my ability but do not constitute tax or legal advice.