Probably the Lamanites did not understand the backlash effect of giving Amulon power over Alma’s people. It was in the Lamanites’ best interests to have a docile population steadily producing their annual tribute. Amulon’s excessive burdens caused such tremendous strain that eventually Alma’s people fled, depriving the Lamanites of a tribute-paying, dependent city. It also seems unlikely that the Lamanites would know about the previous history shared by Amulon and Alma and therefore did not see it as enflaming a previous animosity. More likely, they intended this rule to be more compatible than having a Lamanite overseer—enhancing their long-term access to tribute, not potentially disrupting it.
But Amulon is conducting a personal vendetta. While both Alma and Amulon had ended up as leaders of sub-groups, Alma’s was larger and more prosperous. Amulon would naturally be jealous, in addition to seeing Alma’s rejection of Noah’s religious status quo as leading to his (Amulon’s) personal downfall. In short, this passage reveals the all-too-human tendency to wreak revenge for imagined wrongs.