It appears that there are some details that you omitted in your original question.
Does the 2018 Form IL-1040 that you filed show a refund on line 36 or does it show an amount you owe on line 39? If it shows an amount you owe, did you pay it? When did you pay it?
On your 2018 Form IL-1040 is the Nonresident box checked on line D?
When did you file your 2018 nonresident Illinois tax return?
What was the $250 refund that you say you received? Was it a federal refund (from the IRS) or was it a state refund from Illinois? The Illinois state tax would not reduce your federal refund.
What is the number of the notice or letter that says you owe $1,500? It starts with IDOR or LTR.
Did you receive any other notices or letters from the Illinois Department of Revenue prior to the one that now says you owe $1,500?
Again note that you do have to pay Illinois tax on income that you earned for working in Illinois, even though you were never an Illinois resident, and you lived in a state that does not have state income tax.
Don't mix up a return and a refund. Your tax return is the form you send to the government that shows your income and calculates your tax. The money the government sends back to you is your refund. You don't get a return, you get a refund.
