The scattering Nephi refers to is the scattering of Judah. The Assyrian conquest assured the scattering of the ten tribes, but that is not Nephi's theme. Nephi's people do not see themselves in the gathering of the ten tribes, but rather as part of the gathering of Judah required by the dispersion of the Jews after the Babylonian conquest.
Polemical: One of the charges leveled against the Book of Mormon is that it answers an 18th century question in a way typical of the times. Very specifically, the Book of Mormon is seen in the context of a work like View of the Hebrews which attempts to locate the lost ten tribes in the Americas. While there might be superficial and tangential similarities, the attribution to the Book of Mormon the idea of finding the lost ten tribes derives from a cursory reading of the text, not from the text itself. The Book of Mormon very specifically ignores the question of the ten tribes, and deals with a completely different historical dispersion/gathering.