Income

States with an income tax can tax non-residents on income from work actually (physically) performed within their borders.  However, you only need to file a non-resident state tax return if your income in that state exceeded its filing threshold for non-residents.

You can find a state's non-resident filing threshold on its state tax website.

Section 7 of Public Law 101-322 provides an exception for interstate truckdrivers and rail carrier employees, who are subject to income tax only by their legal state of residence.

https://www.govinfo.gov/content/pkg/STATUTE-104/pdf/STATUTE-104-Pg295.pdf

Talk to the employer ... they should be withholding the state taxes where you are working automatically  or at least reporting how much you made in which states on the W-2 form they issue in January so you have the info needed to file the proper non resident state returns.