Federal and state refunds come from completely separate entities, There is no rule as to which one will come first or how much time there will be between their arrivals. Your state return could not have been e-filed or accepted unless the IRS accepted your federal return, so you might be using the wrong information on the IRS site.
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
https://ttlc.intuit.com/questions/2584108-why-is-there-no-record-of-my-return-at-where-s-my-refund-w...
Sometimes people get confused by the “summary” given by TurboTax and use the wrong amount for the federal refund. Make sure you are only using the federal refund amount, and not an amount that combined your federal and state refunds.
Your federal refund amount is on line 35a of your Form 1040
https://www.irs.gov/refunds
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**