You are correct - working remotely out of state for a few weeks will not change your state tax situation.
As long as you remain a legal resident of OH, you would only have to file an OH return and pay OH tax on those earnings.
If you worked from KY for a longer period of time (several months?), your earnings might exceed KY's income threshold for filing a KY return.
From KY DOR website Do I Need to File a Return
