This portion of Nephi's vision varies from Lehi's vision of the Tree of Life, but fits in perfectly with Lehi's first vision in 1 Ne 1. It may be that the Lord provided Nephi a double-dose of vision, combining Lehi's two visions in one for him.
The concept of Christ coming down, followed by his apostles
(cf Ascension of Isaiah 11) suggests that Lehi, Nephi and Isaiah had similar theophanies/visions.