Here Mormon is describing a process, not a single event. With no clear transition, Mormon has moved from the public reading of records to the installation of Alma as an authorized preacher who moves among the people, teaching. Clearly Alma is moving from one group to another here, and this appears to indicate some time period after the formal gathering. It also suggests that it was still during this festival, as the "bodies" would be gathered only for such a festival. Therefore, what Mosiah has done is bring everyone together, and read to them as a whole. He then introduces (and probably explicitly approves) Alma and sends Alma to preach to them in groups. These groups are at least Nephites, Mulekites, and Limhites (based on Mosiah 25:4 and the specific address to Limhi's people which follows immediately).
It is possible that the preaching to these major political groups has more than a simple religious purpose. Remembering that religion and politics were intertwined in the ancient world, Alma is probably establishing his religious authority with the leadership of the individual groups. The multiple kin organizations of Mesoamerica typically had their own hierarchies of leadership, and Alma's mission is likely to have been to establish his credentials with those leaders. This is a preliminary to Alma's reformation of Nephite religious practices. That coming step would be impossible without widespread support from the kin group leaders.