Whenever an inmate turns himself into a county jail and is transferred to state prison, how did they get the money left over on their commissary account at the county jail

Money on the books at the county jail is not transferrable in traditional ways. The inmate has to request a check for the remaining balance to be sent to their home address. Adding money to an inmate account in a State Prison starts anew, with new funds. If the inmate gets moved within the State system, the funds will transfer from facility to facility.