What should the Jewish believers have told Jerusalem after leaving Cornelius' house?
They should have spread the word in Jerusalem that God was now ready to turn to the Gentiles without Israel. They should have reported that God was dealing with Gentiles on His own ground, not on the basis of using the nation of Israel, and without requiring Gentile proselyte conversion.
Les explains that the sign was particularly used to convince these Jews, because from Cornelius' house the Jews would go right back to Jerusalem. What should they have done? They should have just spread the word that God is now ready to turn to the Gentiles without Israel. But they did not. Les points out that when you go back to Acts chapter 15, Peter and those who evidently went with him had never said a word for another eight or ten years. Not one word did they cast among the children of Israel that God was now dealing with the Gentiles on His own ground and not on the basis of using the nation of Israel.