You'll file a non-resident Kansas state return first and allocate the income you earned for those 25 days you worked in Kansas
Next, you'll file a resident Missouri state return and allocate all your income.
The Missouri return will give you credit for the Kansas tax you paid on that 25 days of income so that you are not double-taxed.
If your employer withheld only Kansas state tax, you should get a refund for the majority of that Kansas state tax and you'll owe Missouri tax that wasn't properly withheld and paid.
State taxes are withheld and paid quarterly, so I assume your employer corrected your future withholding, but they can't get the money BACK from Kansas and send it to Missouri, you need to reconcile that on your state returns.
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