Federal and state refunds come from completely separate entities. You cannot expect them to arrive at the same time.
TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.
You need your filing status, your Social Security number and the exact amount (line 20a of your Form 1040) of your federal refund to track your Federal refund:
To track your state refund: