TurboTax has no control over your state deducting taxes owed from your account. TurboTax only transmits the bank information you entered in your tax return.
You can double check you make sure your state return was accepted if you e-filed. If it is accepted then for some reason your state has not deducted the payment. You can check your return to make sure the correct banking information was entered.
How do I check my e-file status?
