Nephi explains to his brothers what they did not understand. Nephi certainly is explaining information which he received during his vision, but it is interesting to note that the imagery of the olive branch was not part of his vision. While Nephi is correct in his explanation, how did he so rapidly translate his prophetic vision into the context of the allegory?
There are two explanations, either of which can easily explain the situation. It may be that although Laman and Lemuel had not read the Zenos allegory on the brass plates, that Nephi had. That would have provided Nephi with the background context to understand that his vision and the allegory treated the same subject. The second possiblity is that with the clear understanding of the future history of the world, the symbol simply fell into place into his mind. Having seen the future history, the allusion to it had become quite clear.