While a taxpayer's state of residence has the right to tax all earnings, wherever sourced, all other states retain their right to tax income earned within their borders. So, if your son performed work in Illinois, the State of Illinois can tax that income. His home state will also tax those earnings, but will probably also offer a credit for the tax paid to Illinois.
If your son had a sufficiently large income to trigger a filing requirement in Illinois, he is likely going to owe some state income tax. Without knowing specifics (which should never be revealed in this public forum) I cannot comment on the amount of tax, or whether a refund would be appropriate.
