How do I know if my tax return has been processed

TT send you an email once your return has been submitted, and then a second one once accepted or rejected.

https://www.irs.gov/refunds/what-to-expect-for-refunds-this-year

https://www.irs.gov/individuals/refund-timing

When you click the TRANSMIT NOW button and successfully work through the screens that follow, you will receive TWO e-mails from TurboTax

 - The first email informs you that you have SUCCESSFULLY TRANSMITTED your return to the IRS. It can be up to 48 hours before your receive the 2nd E-mail.
 - The second e-mail informs you that your return has either been ACCEPTED by the IRS or REJECTED by the IRS.

• If rejected, you can follow the link in that e-mail to find out why and what you need to fix. Then you just re-submit your return by clicking the TRANSMIT NOW button again.
• If accepted by the IRS, then you are done filing and Turbotax has fulfilled their obligation to provide the services you paid for. 

Once TurboTax fulfilled their obligations, you can track your refund status at https://www.irs.gov/refunds  It can take up to 72 hours after your return is accepted by the IRS, before you will be able to track your refund status.