The killings went in some synchronicity, but some uncertainties had to be taken into calculation. For example, Neri had to improvise when carrying out the killing of Barzini, because the driver didn't go away.
I'm not so sure if that was improvising. I think they expected the driver to not go away. His boss, Barzini, was more important than a fine that could easily be disposed. Barzini had at that stage probably also police and politicians in his pocket. That the driver waited in the car before the supreme court speaks for itself. They never expect someone like Neri, who used this opportunity to stall time.
In the novel Barzini doesn't come out of a court. Neri waits for him at the Rockefeller Center.
Neri is too early. Then he wants to send the car away. ( I guess because he wants to reduce the risk.)
" “Let me see your license and registration,” Neri said. He had been hoping to get the driver to go around the block but there was no hope for that now. Out of the corner of his eye, Neri saw three short, heavyset men coming down the steps of the Plaza building, coming down toward the street. It was Barzini himself and his two bodyguards, on their way to meet Michael Corleone."
(...)
"He put three bullets in Barzini’s barrel chest before the other three men unfroze enough to dive for cover. By that time Neri had darted into the crowd and around the corner where the car was waiting for him."
It was a highly risky mission.
