Filing state taxes over $1000. Since Kentucky Illinois are reciprocating states, shouldn’t he?

My fiancé works in the state of Kentucky, however, the business he works for is out of Illinois. He did not file his state taxes due to the confusion of which state he had to pay into. He has Illinois taxes, taken out of all of his checks. When we went to file his taxes, it showed that he was going to owe the state of Kentucky over $1000. Since Kentucky and Illinois are reciprocating states, shouldn’t he not have to pay Kentucky? He ended up filing for an extension, which at this point I believe has passed or is coming up. What does he need to do?