Once Turbotax receives the money from the IRS, how long until they send it to you via direct depost?

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

The movement from the IRS to the third party bank  to your bank account can take up to 3 business days to happen although it can take longer or shorter.