Tessio indirectly betrayed deceased Vito by directly betraying the living Michael?
You could say that. Tess disobeyed Vito's command (in the fishtank scene) to "be a friend to Michael." But, he waited until after Vito died to make his deal with Barzini
Don't know Turnbull I reckon he went straight to Barzini from the fishtank scene and made his deal before Vito died
I too believe Tessio had made his deal with Barzini when Vito was alive
Barzini and Michael's meeting to straighten any of their problems out! was already arranged before Vito's funeral