In answer to your inquiry, please refer to the following post (simply click to open):
https://ttlc.intuit.com/questions/3630265
The detailed information provided there is for a Texas taxpayer with an almost identical situation to yours. The only difference in your answer will be the actual employer state involved. Simply substitute Illinois, where appropriate, in the wording of that other answer.
Your conclusion will be identical. You will not have to file a personal state income tax return (in Illinois, or Texas), or pay individual income tax in either state. You will only have federal income taxes.
Thank you for asking this important question.