Yes, when your RSU vests it would be considered unearned income in the state where you reside when you receive it.
When you receive an RSU, you don't have any immediate tax liability. You only have to pay taxes when your RSU vests and you receive an actual payout of stock shares. At that point, you have to report income based on the fair market value of the stock.
Click this link for more info on RSUs or Stock Grants.
This link gives details on How to Allocate Income for a Part Year Resident .
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