It depends. The Service Member Civil Relief Act states that an active duty member is not considered a resident of a state unless it is his SLR. Therefore, if Illinois is your State of Legal Residence (or HOR), then you may owe taxes to the state. Every state is different in how they tax active duty military members (see more info in the bottom link). But, if Illinois is not your SLR, then you should not have to file taxes in that state unless you had a civilian job in the state.
Within the My Info section of TurboTax (select from black column on left side of screen), be sure that you have selected that you are active duty military and that the "state lived in" field is your State of Legal Residence (SLR) and not the state where you are currently stationed (unless it is the same as your SLR).
Here is more information:
https://ttlc.intuit.com/replies/3302301
https://ttlc.intuit.com/replies/3299939
