I agree with both. Clearly Barzini would know that a guy who turned on his long-term Godfather would be an immediate security risk to his new boss or patron. And, having gotten rid of Michael (and presumably Clemenza), why would Barzini tolerate even a semblance of independence from Tessio? So I agree that he would have dispatched Tess sooner rather than later.
I remember I already said this in another topic. But a scenario such like this happened in real life. Cesare Bonventre, Carmine Galante's bodyguard, conpsired with Galante's enemies to take him out. After that, he was promised to become a caporegime of the crew of zips. He did become a caporegime, but was killed a few years later anyway. I'm not sure about the exact reason for this, but I remember reading/hearing that it had something to do with him betraying Galante. He was therefore considered unreliable.
