This part comes right after the description of the killing of Barzini:
Hagen said. “You better make your call to Barzini and tell him to start on his way.”
Tessio rose and went to the wall phone. He dialed Barzini’s office in New York and said curtly, “We’re on our way to Brooklyn.” He hung up and smiled at Hagen. “I hope Mike can get us a good deal tonight.”
By then the people in Barzini's office might have known about Barzini's death.
So Tessio must have been killed first.
How the hell did the Corleones organize all this without mobile phones?
