@callmeselby --
Regardless of your residency, MA can tax the unemployment compensation that you earned by working in MA.
You're considered a resident of MA for tax purposes until you abandon your domicile in MA and establish it in WA. Your domicile is your main, primary home. You can have only one domicile at a time. You establish a new domicile when you begin living in the new location and show by your actions that you intend to make it your new main home. MA can tax all the income you earn as a legal resident of MA, regardless of the income's source.
From your description ("I relocated to WA in August") it appears that you abandoned your MA domicile and established your WA domicile in August. If so, MA would be able to tax 100% of your unemployment compensation, plus 100% of the income you earned prior to August.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
