I paid to get my State refund electronically deposited into my account. It was sent via post office mail. How do I get reimbursed?

The fee is for preparing the return. TurboTax has no information about the return after it’s filed. Why you got a check instead of direct deposit is a question for the state, not TuboTax. 

There is no fee to get a Direct Deposit or to get a fast refund.  The fees are only to prepare the return.  If the IRS or state couldn't deposit it or the bank rejected it then they will mail a check to the address on your return.  That's very common.  

And if you used the Desktop program and paid the fee to efile state that was only to submit the state return.  Nobody can guarantee a Direct Deposit.