It's not a generally disputed principle that one person's good work can provide blessings for another. The good you do can help the progress of your family, friends, and the world, although they have to choose whether they will receive the blessings.
Likewise, the Savior performed the ultimate vicarious work. Because of His Atonement, we have the opportunity to enjoy eternal happiness and eternal progression. But it is still our choice whether we will receive it. The efficacy of vicarious work is dependent on the receiver.