You filed returns for two different states? Some states process returns and send refunds faster than others.
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.
STATE RETURN
Make sure your state return was accepted: https://turbotax.intuit.com/tax-tools/efile-status-lookup/
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
I had to file 2 because I lived part year in Indiana and the other in Michigan because I moved to Michigan.
Yes, if you are due refunds from both states, they should each send you the refund.
Michigan and Indiana have a reciprocal agreement which means you pay tax to the state in which you live even if you work in the other state.