It will appear that way because states will typically want you to pay taxes on money you earned in the state and the state where you live will want you to pay taxes on money you earn anywhere while you live in the state. That can lead to a double taxation situation. However, you can claim a credit on your resident state return for taxes paid in other states so that the income earned in the other state is only taxed once.
So, in your situation, if you lived in Missouri all year, you will file a resident return for Missouri. Then, since you only worked in Illinois, you will file a non-resident return for Illinois. Complete the Illinois return first. Then work on your Missouri return and watch for an option to claim a credit for taxes paid to another state. This will give you credit for the taxes paid to Illinois and TurboTax should pull all the numbers into the form for you.
To learn more, take a look at the following TurboTax article:
Multiple States—Figuring What's Owed When You Live and Work in More Than One State
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