The email that says they have been accepted, means that the transmittal of the e-file was accepted or received by the IRS, after is received it gets accepted or rejected.
If you still get the emails your return might still be rejected by the IRS. Please log into your TurboTax account and see the reason as to why is being rejected and click on the fix me button.
I believe the email that you received should say on the bottom under the fix me button, If you have already fixed it disregard. And if you happen to click without disregarding in keeps creating another email. I will submit this issue to our team.
Thank you for reporting it. We appreciate your input and your business.