Turbo Tax does not say approved. It says Accepted or Rejected. If it was Accepted then the IRS got it and then processes it. Then the IRS Approves it. Yes It will go to your refund method.
If you used the Online version you can check your efile status here
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
When you efile you get back 2 emails. The first email only confirms the transmission. The second email says if the IRS (or state) Accepted or Rejected your efile. And check your spam folder for them.
When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. What does it say?
Approved? Sounds like a credit card or other payment method approval to me.
When you e-file your tax return the first message you get is that the tax return was "successfully sent". You also get an e-mail telling you that, if you provided an e-mail address.
Later, when you start up the TTX program again to check the status, that status will be either "Accepted" or "Rejected". You also get an e-mail telling to that, if your provided an e-mail address.
So just exactly what is "approved"?
Could it be a response for your state tax return maybe? I can't say on that front since my state doesn't tax personal income. But if so, you might want to mention which state.
Take note also that absolutely nothing is filed until "AFTER" you click the big orange "TRANSMIT MY RETURNS NOW" button.