Perhaps the false prophets, preachers, and teachers are simply an expansion on the category if "false Christs" or perhaps these are yet others who were championing the competing religion. In any case, their presence cause tremendous upheaval in Zarahemla, which we read between the lines of Mormon's terse account. First we note that the contentions are so severe that punishment of "crimes" occurs. Of course in the ancient world rulership and religion were not far separated, and the presence of a competing religious structure probably also threatened the political structure, hence the "crimes."
Next, however, we note that there were "many dissensions away unto the Lamanites." Everything we see about these particular contentions is based on religion, and the solution for many who were unable to accept the newly imposed religious/political regime left Zarahemla - and went to the Lamanites. In terms of the Book of Mormon, that would be logical because there was no other named people to whom to turn. However, we might doubt that they went to the very people who were defeated in battle not long before this. Nevertheless, they did go to some "Lamanite" (read non-Nephite) group. Given the religious cause of the dissention, we may suppose that they left to go to a group of people following the more common religion of the land, though probably not the Lamanites in the land of Nephi, who would have a different language, and slightly different religious system. These dissenters would have gone back towards the old Jaredite homeland (Olmec lands in Mesoamerican terms) which fit with their linguistic and cultural heritage.