I filed my tax return Feb 1st and it was accepted the following day. I was delayed because I had to send in requested information and just now approved on my refund May 4

Will my refund still go through Santa Barbara tax product group and then to my account like it always does so that TurboTax gets paid?

Yes if you selected to have the fees deducted from your refund.  But if it takes the IRS too long to send your refund then the sbtpg bank will take the fees out of your account.  They will send you several emails before debiting your account.  Then when the refund comes through they won't take the fees out again.

Seems like they would have taken the fees from your account by now if you got accepted back on Feb 1.  Or did you pay the fees upfront this time with a credit card?