Matter of fact, I believe that it was quite the opposite. Barzini was the one who probably had a back up plan to take out Tessio had they succeeded in assassinating Michael. Barzini's thinking:

"Now how can I ever trust a man who is willing to set up and sell out the Corleone family...a family that he has been with since the beginning? If he was willing to turn on Vito and his son, a family that has been loyal to him, then who am I? Surely he won't think twice about turning on me if the opportunity presents itself."

I believe that Barzini made all kinds of promises to Tessio and never intended on keeping them. He was going to take Tessio out as soon as he, Barzini, became the new Boss of Bosses.