When you do two part-year returns, you should do the nonresident state return first and then the one where you lived at the end of the year. TurboTax will then transfer this information for you from the first return tot he second.
Basically, you would have no double taxed income on part-year returns if you changed jobs when you moved. If you moved and continued working for the same company but forgot to tell them you lived in a different state now, they may have continued withholding for the old state after you moved. That's what double taxed income means. It is confusing though and that's why it's best to let the program do this part for you. Following are instructions on how to remove the states if you did them in an incorrect order. You can then start them over.
https://ttlc.intuit.com/replies/3301384
