Yes, if you are a Kentucky resident, you must file a resident return and report and pay taxes on all your worldwide income. That pays for the privilege of living in Kentucky (public services, etc.) However, under the terms of a number of cross-state agreements, you get a credit in KY for taxes paid in other states for income earned in those states.
The practical effect is that the net tax you pay is the higher of each state you work in. For example, suppose you earned $10,000 in MT and $10,000 in PA. MT tax is 3%, you pay $300. PA tax is 7%, you pay $700. KY tax is 4%, you would normally pay $800. In this case, for the MT income you owe $400 in KY tax but get a $300 credit, so KY taxes you an extra $100. You would also owe $400 on your PA income. Since you already paid $700 to PA, you get a credit for that and don't have to pay anything to KY, but you don't get money back from KY just because PA charges a higher rate. So you end up paying $300 to MT, $700 to PA, and $100 to KY.
