Yes, report wages as indicated on your W-2. Your employer was correct, TurboTax will take care of this when you file the state returns.
You need to file 2 part year resident resident returns - one for MN and one for CO. I will leave the full instruction link below. On the W-2 entry screen, enter exactly what is on your W-2. When you go through each state return, you will be able to allocate (see link below) the correct amount of wages that belong to each state. The income belongs in the state you were physically working in when you earned the income.
TurboTax handles part-year returns, but you need to make sure you've set up your personal information correctly for us to do so. We'll ask about where you lived in 2021 when you set up your personal information. Full instructions for filing part-year resident returns
How do I allocate (split) income for a part-year state return?
How does TurboTax calculate taxes on part-year returns?
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