Did you request to have your fees deducted from your tax refund? If so, the IRS sends the refund to a third party bank who remove the fees and send the remainder to you.
Not sure why you think your refund went to someone else's account. The refund goes to the account that you entered when you prepared your tax return unless you entered incorrect information. If you entered incorrect information, then the bank will reject the deposit and send it back to the IRS. Then the IRS has to issue and mail a check to the address you entered on your tax return.
if you chose to have your TurboTax fees deducted from your federal refund then the banking information on the tax form is the information to send your refund to the third party bank. That bank gets your refund first from the IRS. They take out your TurboTax fees and send the rest to you---and that bank has YOUR direct deposit information.
When you choose "refund processing" TurboTax gets its fees when the IRS releases your refund. Your refund goes to the third party bank. The bank takes out your fees and then that bank sends the rest of the refund to you.
How can I see my TurboTax fees?
https://ttlc.intuit.com/questions/2565973-how-do-i-review-my-fees-in-turbotax-online
What is Refund Processing Service?
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