We cannot be certain that the Lamanites understood that this would happen when they placed Amulon in a position of power of Alma and his people, but it is not likely that they did.
We must remember that it is in the best interests of the Lamanites to have a docile population working to provide the tribute exacted from them.
The excessive burdens Amulon places upon Alma's people will lead to tremendous strain, and eventually the abandonment of the area by Alma's people. For the Lamanites, this will cost them a tribute-paying dependent city, and they are the poorer for it.
The Lamanites would probably not have heard about the specific problems that Amulon would have with Alma, and therefore could not even guess that there would be a previous animosity that would be exacerbated. It is more probable that they intended this rulership by "an old friend" to be a better arrangement than having a Lamanite overseer. They would have seen it as enhancing their long term access to tribute, not as a potential disruption of it.
For Amulon, this is a story of personal vendetta. While both Alma and Amulon had ended up leading a group of people, Alma's was larger and more prosperous (perhaps due to its size) than was that of Amulon. Thus Amulon would see Alma as a representation of all that had lead to his personal downfall.
Unfortunately, we have in these verses the all-too-human tendency to malicious revenge for imagined wrongs.