TurboTax never tells you that your state refund has been paid, so you misunderstood something. TT never gets feedback from the state and never knows if your state refund was paid or if you paid your tax due.
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. Some states process returns quickly and some are very slow.
STATE RETURN
Make sure your state return was accepted: https://turbotax.intuit.com/tax-tools/efile-status-lookup/
To track your state refund:
ttps://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_US_en_US?uid=lt447ebr
Once your return is accepted for processing by the IRS and/or State TurboTax has no control over the processing of your return and/or release of your refund. If you have any inquiries regarding any delay you should contact the IRS or your state Department of revenue directly for further assistance.
There is a couple of FAQs to help you track your refund
When will I get my federal tax refund?
How do I track my state refund?
Why does Where's My Refund say "approved" but TurboTax still says "accepted"?
Why do some refunds take longer than others?
What if my IRS refund is taking longer than 21 days?