Check your spam folder to make sure your e-file results did not go there.
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:
If the IRS accepted it, what does it say here?
https://www.irs.gov/refunds Or does your account say “Ready to Mail?”
Not quite sure, but I don't think taxes filed by October 15 based on an extension provided in April can be e-filed. I think they want you to file extension-allowed returns by mail. In that case, the post-mark provides evidence the return was filed on time (before Oct. 15). They might take awhile getting around to looking at your hard-copy return, and therefore might not accept it right away. I think Turbo Tax works in that way and does not give you the option of e-filing taxes when Turbo Tax previously submitted your extension request. If you e-filed late but without an extension, you are significantly late no matter what you do now.
None of the above answers seem to respond to the question: if I e-filed by October 15th but had the return rejected, how long do I have to refile? And do I have to mail both of my returns?