Your tax refund was not sent to TurboTax. TurboTax does not handle your refund at all.
Santa Barbara Tax Products Group, LLC (SBTPG) is the bank that handles the Refund Processing Service when you choose to have your TurboTax fees deducted from your refund. This option also has an additional charge from the bank that processes the transaction.
You can contact them SBTPG, toll-free, at 1-877-908-7228 or go to their secure website www.sbtpg.com
https://ttlc.intuit.com/questions/2580357-who-provides-the-refund-processing-service
https://ttlc.intuit.com/community/refunds/help/who-provides-pay-with-my-refund/00/26410
And....the third party bank does not handle your state refund at all.
Federal and state refunds come from completely separate entities, There is no rule as to which one will come first or how much time there will be between their arrivals.
STATE RETURN
Make sure your state return was accepted: https://turbotax.intuit.com/tax-tools/efile-status-lookup/
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund