California has a good publication. You can see it as html https://www.ftb.ca.gov/file/personal/filing-situations/military.html or pdf https://www.ftb.ca.gov/forms/2018/18_1032.pdf

I sure Oregon has similar pubs. 

The way it works in general is you will get a credit in one state for the tax paid in the other. There is no double tax, but a client will likely end up with the higher of the two taxes. If you set up the software correctly it should go fairly smooth. You do need  to read carefully to set up the software.