Equity compensation that was granted in non-resident state

Hello,

 

In 2019 I had equity compensation that was granted while working in STATE A and exercised while working in STATE B. I live in STATE B now. Both states require equity compensation that is earned in more than one state to be allocated amongst the states according to the time spent in each state during the grant to vest period. Currently, my W-2 shows that all of this income was made in STATE B.

 

Do I need to file state taxes in both STATE A and STATE B? If that is so, do I need to reduce my income when reporting my income on the W-2? Or will filing STATE A automatically adjust that and credit me the tax amount?