Each state has rules that differ from the federal government's.
Although for federal purposes, your son would not pay tax on $4021 earned income, the state of Illinois rules differ. Regarding who must pay tax in Illinois,
[If you are] a student,you are not exempt from tax nor are there special residency provisions for you. However, income, such as certain scholarships or fellowships, that is not taxable under federal income tax law, is also not taxed by Illinois.
Illinois does not have a standard deduction, but only a personal exemption. Your son's is $2175, but as a part-year resident, he would only qualify for a portion of that based upon the percent of his income earned in Illinois. Illinois's tax rate is a flat 3.75%, so he would owe $69 in tax if he were an Illinois resident, and more if he earned money in any other state, because his personal exemption would be reduced.
Illinois does have reciprocal tax agreements with Wisconsin, Michigan, Iowa and Kentucky, which means that residents of these states who work in Illinois are taxed by their state of residence, not by Illinois. But as a student living and working in Illinois, he would count as an Illinois part-year resident.
Illinois income
tax instructions can be found here.
