Is it correct that my state taxable income for a new state I moved to be a combo of the previous state and new state?

AZ Form 140PY asks for your total federal income in order to determine your tax rate, but it actually taxes only your AZ income.

You must manually allocate your income.  Arizona income is what was actually paid to you when you were living in Arizona (including bank interest, investments, and so on).  Colorado income is income earned while living in Colorado.  Turbotax might try and guess based on your W-2s but it won't know how to allocate other types of income, and it might be wrong about the W-2s depending on when you moved and when you were paid.

That being said, the states often need to know what your total income was, even though they will only actually tax the in-state income (California is the same way). 

When allocating your income, you'll need to determine if the income is earned or unearned, as these are handled differently:

• Earned income comes from employment, such as wages, salaries, tips, payment for services, and commissions
• Unearned income comes from non-employment sources, such as interest, dividends, capital gains, social security, and IRA distributions

Select the income you need to allocate and follow the instructions from the link below:

How do I allocate (split) income for a part-year state return?