Yes. You report all of your income on your home state's return. You will get a credit for some or all of the taxes that you paid to SD on your IL return, however. This prevents double-taxation.
For the smoothest results, work on your SD nonresident return first inside of Turbo Tax; then go through Illinois. The Credit for Taxes Paid to Another State will be a prominent category inside of the Illinois interview in Turbo Tax, so just make sure you go through these screens.
