I opted to pay fees out of my refund. Refund took months to approve and turbo took the money out of my account on May 18th. Will my refund still go through Sbtpg?

Yes your refund will still go through the third party bank but your fees will not be deducted again if your account has been debited already.

If you originally chose to pay your TurboTax fees out of your Federal refund, that process is handled by an intermediary company SBTPG (Tax Products Group).    With that method the IRS sends your refund to a temporary bank account set up in your name at an intermediary bank where the fees normally would be subtracted (when there is not an unusually long delay at the IRS like you've experienced).  Then that intermediary bank would send the rest of the funds to your bank (or card) in a second direct deposit.

The fact that you have now been debited for the fee won't make any difference on the route of your funds once they are sent by the IRS.   The only account info the IRS has is the routing and account number for your temporary account at the intermediary bank, so it will still go to SBTPG's bank first.   That bank will send the funds to your bank account (or card) in a second direct deposit.

Once the IRS has released and sent your refund, you can monitor the status at SBTPG's website.

https://www.sbtpg.com/

At that page choose the "For Taxpayers" portal.  Then on the next page choose "Check with TPG."

Yes, the federal tax refund will still be sent to SBTPG since that is the bank routing and account number received by the IRS.  SBTPG will send the refund to your bank for direct deposit.  

See this TurboTax support FAQ for payment of the account fees - https://ttlc.intuit.com/community/charges-and-fees/help/why-was-my-bank-account-auto-debited-for-turbotax-fees/01/26102

Santa Barbara Tax Product Group website - https://www.sbtpg.com/

Tax Products Group Contact Information - https://help.sbtpg.com/hc/en-us/articles/230084587-Contact-Information