Jones turned himself in this morning.
He was taken to a hospital and died on Tuesday.
When the man allegedly banged on Jones' vehicle, the second-year Wake Forest coach reportedly punched him.
After he punched Szabo, police say Jones got into an SUV and drove away leaving the man on the pavement. They say the punch caused Szabo to fall and hit his head on a sidewalk.
Jones was released on his own recognizance and ordered to return to court October 2. His attorney calls the encounter a "tragic accident". Szabo had been treated for fractures to the left side of his face and the back of his head, and for bleeding on the brain, according to the complaint filed against Jones.
"We have just been made aware of this matter and we are gathering information", Wake Forrest said in a statement to USA TODAY Sports.
The investigation is ongoing, and charges against Jones could be upgraded, police said.
Jones joined the Demon Deacons staff last May after previous jobs at UCF, VCU and Florida Gulf Coast. The Philadelphia native is a 2008 graduate of Arkansas Tech.
Mr Szabo's family said he was in New York City to attend a wedding. "Sandor was super outgoing, friendly, and an incredibly smart businessman". He was fun to be with, interesting, and always interested.
"His lovely spirit and his love of life will remain with us", the company said. "We are going to miss him dearly".