Once a tax return has been Accepted by the IRS or a State, TurboTax receives no further information concerning the tax return or the status of any tax refund.
Federal and state tax refunds are sent from totally separate tax authorities.
Only the IRS and your State control when and if a Federal or State tax refund is Approved and Issued.
If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds
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
Federal and state are separate and come at different times. Only the IRS can tell you. They don't update Turbo Tax when they send your refund. What does the IRS say at Where’s My Refund
https://www.irs.gov/refunds