Barzini certainly wouldn't have had confidence in Tessio as a loyal soldier, but nor as an outright traitor. We see that the new york families, including the Barzini family, are very business minded, there is less of a "personal" aspect involved. Barzini would have regarded Tessio as a man making the correct business decision: the Corleone's are losing, and Tessio knows it's smarter to join Barzini. Barzini wouldn't feel too threatened by Tessio until he was vulnerable to attack, after all, Tessio probably wouldn't sell him out in the future unless he was in a similar predicament to Mike's. But doubtless he would not have trusted Tessio much anyway.