"Does he have to file a WI tax return?"
The Wisconsin-Illinois reciprocity agreement applies only to wage and salary (W-2) income. It does not apply to self-employed income.
Wisconsin can tax a non-resident on self-employed income earned from work actually (physically) performed in Wisconsin. Therefore the portion of the taxpayer's income earned when he works at the Wisconsin office is taxable by Wisconsin. He must file a Wisconsin non-resident tax return if his income exceeds Wisconsin's filing threshold for non-residents, which is detailed here:
https://www.revenue.wi.gov/Pages/FAQS/pcs-indreq.aspx#:~:text=a%20tax%20return.-,As%20a%20nonresident%2C%20why%20am%20I%20receiving%20a%20notice%20to,means%20income%20before%20deducting%20expenses.