No, as a WI resident, WI gets to tax all of your income regardless of where it comes from. To prevent double taxation, your TT/WI return will prepare a Other State Tax Credit for you for some or all of the IL tax on the income that both states are taxing.
To make that happen, prepare the nonresident TT/IL return first. Then TT/WI can get the info it needs to prepare that credit from the completed TT/IL return.
