You only have to pay income tax to your home state. You only have to file a return to your home state (not your employers state). https://www.gpo.gov/fdsys/pkg/USCODE-2009-title46/html/USCODE-2009-title46-subtitleII-partG-chap111-sec11108.htm
I know someone who pays partial to the state where he is employed because he can use that amount to offset his home-state taxes, but that only works if your employer’s state has a lower tax rate than your home state. Pretty complicated and I bet any tax savings is offset by preparers fees.