Turbotax is calculating this correctly. Your resident state taxes all of your income no matter where you earned it at. Illinois can tax the income because it is considered as "Illinois Source" income. California does allow you to claim a credit for the taxes you pay to Illinois on this income, but, as you mention, California tax is higher, so they still receive a balance of what they tax the income after crediting what Illinois taxes the income.
Even if you could prorate the expense, California would still be allowed to tax all of the income because that's where you live when you receive it, and therefore your end tax result wouldn't change.
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