If the status of the tax returns on the TurboTax Tax Home web page indicates Accepted, then your tax returns were e-filed - https://myturbotax.intuit.com/

You may have more than one account on TurboTax, so the email may be referencing the other account.  Disregard the email if your tax returns are Accepted.

If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds
If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions