TurboTax has no control over state policies. Some returns are chosen at random for security checks. The state is making sure that you are the one in possession of that W-2.
Accepted only means the state found no reason to reject the return on its initial check. That check does not include everything on your return. after acceptance, the return goes through further verification. perhaps what you entered for state withholding is not what's on the W-2 or perhaps your employer never sent in the W-2s. Most states require that the employer file copies of the state w-2 directly with the state.
Comply with their request for the form ASAP so the return can be processed.
This happens from time to time for reasons the state does not have to explain.
Yes, your employer is required to do this also.
Just because the state or the IRS accepted your return as filed, does not mean they agree with it. While not common, it is not unheard of for the IRS or the state to request you send them documents to justify/verify your return. Follow the instructions in the letter you got from the state to absolute perfection. Do no more or no less than "exactly" what that letter tells you.