Once your returns are accepted, only the IRS and State would know when you will receive your refund. TurboTax does not get any information about your refund.
You can check the IRS website Where's My Refund for your Federal information?
https://www.irs.gov/refunds
If you have a State refund, click on the following link, then click on your State
https://ttlc.intuit.com/community/refund-status/help