To the Lamanites, these people that are heroic to the Nephites would be seen as traitors. The rejection of Lamanite religion, and the rejection of the previous polities would suggest that there would be hatred towards them. When we also remember that it was an Amalikite-led revolution that drove the people of Anti-Nephi-Lehi from their land, we have a political rivalry as well.
The people of Anti-Nephi-Lehi contained a previous king of the Lamanites, and therefore a legitimate ruling lineage. This is a dangerous thing in the Mesoamerican world, and indeed among all kingships. The possibility of a legitimate claim upon the throne from someone else was a risk that most peoples of the world found a way to remove, usually through sad violence. It would appear to have been the same in this case. There were numerous reasons why the Amalekites would be particularly interested in the destruction of the Anti-Nephi-Lehies, now known as the people of Ammon, and not so coincidentally, residing in Jershon.