The date you'd see on TurboTax Refund Tracker is just an
estimated date based on when other customers have filed. But you can find that tracker here
https://turbotax.intuit.com/tax-tools/wheres-my-refund/ You'd have received an email if you were rejected. If you didn't get an email, check the e-file status to see what it says.
If you are using TurboTax desktop product, open the software, click File tab in the very top of computer screen and scroll down to Check E-Filing Status.
And once you have filed successfully using TurboTax, the IRS and/or state handles all processing of the returns and your refunds. TurboTax no longer has any control nor does any processing/handling of the returns and refunds.
And you can use your State Department of Revenue's website to check status of
state tax refund. Choose your state here
How do I track my state refund? and it will give you steps to track the status.