Sollozzo didn't reveal the Tattaglia connection when seeking his meeting with Vito letting Tom discover the connection “My compliments” even otherwise why would "always a pimp" Tattaglia's recommendation carry any weight
That was just Sol's way of buttering up Tom--making him seem like he was a brilliant investigator. In reality, Sol would never have gotten an audience with Vito if he wasn't vouched for by another of the Five Families.
Was having Tessio present at the meeting another Vito slip-up?
Vito's strategy been deliberately keeping Tessio under wraps and Tessio outwardly operating as an 'independent' Family, distanced from the Corleones so that the other Families wouldn't know the Full strength of Vito's Caporegime Yet....
"Tessio under wraps" was a creature of the novel, not a point made in the film. Vito needed Tessio present to hear his unequivocal "no" same as the others,
