Your source clearly says that the likelihood of transmission is reduced, not eliminated.

‘“So even though there are breakthrough infections with vaccinated people, almost always the people are asymptomatic and the level of virus is so low it makes it extremely unlikely — not impossible but very, very low likelihood — that they’re going to transmit it,” Fauci said.‘

Extremely unlikely is a lot stronger than reduced. Calling it breakthrough implies that the norm is prevention. Obviously nothing is 100%.