Not sure.
I recreated your issue. I don't get this message. When I report TN income as a KY resident, the program prompts me to start a TN tax return, but then it tells me I don't need to file it.
Regardless, Tennessee doesn't have state income tax on wages, so you don't need to file a Tennessee state tax return to report her earnings.
As you know, you do need to report this out of state income on her Kentucky state tax return.
