The only specifics we have of Alma's teachings to the groups is that presented to Limhi and his followers.
We cannot tell if this were the last or the first, but it is likely to have been the first. The Limhites are their family, perhaps even literally. They come from the same place, the same set of experiences. Therefore the empathy between the two groups is the highest. It will be the easiest for Alma to establish his innovations first among the Limhites, and then among the rest of the people. Perhaps Mormon gives us this one example rather than all of them because it was the first, and the rest were repetitive of these essentials. In any case, Alma goes to Limhi and his brethren and preaches to them the gospel as it has been revealed to Alma (by Abinadi and the Lord).