Sollozzo inwardly feeling smug that the Corleones have no idea about Barzini connection
One question is why would Sol tell Tom, "The Tattaglia family is behind me with all their people. The other New York Families will go along with anything that will prevent a full-scale war." People make tactical errors, but since Sol is trying to avoid a lengthy war it would make sense to reveal the Barzini connection then, because he would want his side to look as big as possible. The simple explanation is that Barzini wasn't on board, yet.