Yes. All your wages are IL only so zero outside of IL. You will get a credit on your MO return for any taxes withheld on wages there because you allocated all wages out of MO, but answer "yes" there was withholding.
Your other income sources (Interest/dividends/etcetera) are taxed in MO and that is the income that is double taxed and will be used to get a credit on your IL return.
On your MO return, if your other income besides wages was 600+, then answer "Yes"; if not, "No". It's ok to put the duty station name there even if in IL.
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