Always go by the actual date provided on the website as we have no control over your return once the IRS has accepted it for processing.
You might receive an email from TurboTax saying that your refund is "on its way", however you should track your refund directly from the IRS and/or Department of Revenue’s Website. These websites have the most accurate and up to date information and they get updated once a day.
Also Keep in mind that once your return is accepted for processing by the IRS and/or State we have no control over your return. If you have any inquiries on any delay you should contact the IRS or your state Department of revenue directly.
You can also monitor your refund status by clicking on the link below
To track your Federal Refund
Where's my Refund
To track your State Refund
How do I track my state's refund?