How long does it takes for turbo tax to release your refund once you get a date?

TurboTax does not control or even touch your refund.   Your refund is controlled and issued by the IRS.  If you chose to have your TurboTax fees deducted from your refund, the refund goes from the IRS to the third party bank, and then that bank sends the rest of the refund to you.

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