Start by understanding your resident state(s) tax income no matter where it is earned. Typically, your non-resident state only taxes income earned in that state. I say typically because some states have reciprocal tax agreements whereby the non-resident state will not tax income for residents of the reciprocal state. You might repost with the states involved in your situation which will affect how the income is filed. Below is assuming there is no reciprocal agreement.
You will be filing as a part-year resident in states A and B. Yes, you are correct job A while resident in state A is all state A taxed income. However, Job B located in state B is all state B source income and taxed by state B. Further, the period you were still resident in state A while working job B is also taxable by state A. It doesn't matter that you physically worked in state B some days and worked from home in state A others; your resident state taxes the income no matter where it was earned.
After entering your income and deductions in the federal interview work your state B interview. NOTE: The form W2 is entered just as you received it in the federal "Wages & Income" section; you will allocate in the state interviews. After working the state B interview find the total state B income and total state B tax liability in the state tax summary using the steps below and make a note of the amounts; you will need those later.
1. Select "Tax Tools" in the left hand menu
2. Select "Tools"
3. Select "View Tax Summary"
4. Select "Preview My 1040" in the left hand menu
5. Select the applicable state B tax summary.
Now work your state A interview.
Part of the income from job B is allocated to state A based on your residency period. Count the pay periods for job B while still resident of state A and divide that by the total number of pay periods for job B. Multiply that percentage by the W2 Box 1 amount to arrive at the job B income to be allocated/taxed by state A.
Having said that, your resident state A typically offers a credit for taxes paid to another state to mitigate the double taxation. In the credit section of your state A interview you will typically find the credit for taxes paid to another state topic. There you will be asked what was the income double taxed by the state B (enter the amount of job B income you allocated to state A) and the tax on that double taxed income. To find that tax number divide the amount of income allocated to state A by the total state B income (from state B tax summary). Multiply that percentage by the total state B tax liability (from state B tax summary) to arrive at the tax by state B on that double taxed income.
This will get you a credit on your state A return.
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