Did you e-file? Did you click a big orange button that said “Transmit my returns now?”
When you e-file your federal return you will receive two emails from TurboTax. The first one will say that your return was submitted. The second email will tell you if your federal return was accepted or rejected. If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.
First, check your e-file status to see if your return was accepted:
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
If the IRS accepted it, what does it say here?
https://www.irs.gov/refunds
Or does your account say “Ready to Mail?” Or “Rejected?” Or “Printed?”
If you e-filed and you know the IRS has accepted your return, you might have an "old" account that is triggering marketing emails---you can ignore them.