The date you see on the TurboTax Refund Tracker is just an estimated date based on data ranges of others that have filed. It's not going to be exact since it will not take into consideration all the things the government does (i.e. EIC/ACTC delays, possible backlog delays due to IRS being behind on processing, etc). Please see here Why can't TurboTax give me an exact refund date?
For the exact date and the most accurate, you will need to track your status with the IRS and/or your state. They provide the date once they have completed processing your return and approved the refund.
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.