What is the most relevant thing here is that California does not recognize the deductibility of HSA contributions. For California, an HSA is just another investment account and you have to pay tax on the earnings from the account.
Since nearly all the HSA activity was in California, let's talk as if it were 100% California. This gives rise to the following:
1. As soon as TurboTax sees that you made excess HSA contributions, the excess is added back to Other Income on the federal return. The timing is not dependent on when you ask for the distribution.
2. Since HSA contributions are not deductible in California and since all of the contributions were made in California (for purposes of this discussion), all of the contributions made through your employer (i.e. as shown with code W in box 12 of your W-2) are added back automatically to CA state income by TurboTax - you don't have to do anything.
3. As noted, you need to report the earnings of the HSA account as if it were an investment account - this will probably require a special call to your HSA custodian.
If your time in Arizona working for this company was less than 2 weeks, both the CA and AZ returns might be correct "as is" out of TurboTax. If you spent more weeks working in AZ for this CA company, come back and let us know how long it was (in terms of weeks or days), and we'll see if it will make much of a difference and how to enter it.
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