Mormon is describing a process, not a single event. With no clear transition, the action moves from the public reading of records to Alma’s ministry as an authorized preacher, circulating among the people. This process suggests some time period after the formal gathering but still during the festival, as the “large 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 endorses) Alma and sends him to preach to them in groups. These groups consist of 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 preaching to these major political groups has more than a simple religious purpose. Since religion and politics were intertwined in the ancient world, Alma is probably establishing his religious authority with the leaders of the individual groups. The multiple kin organizations of Mesoamerica typically had their own hierarchies of leadership, and Alma probably needed to establish his credentials with those leaders as a prerequisite to reforming Nephite religious practices, since reform would be impossible without widespread support from the kin group leaders.
Variant: This verse began “It came to pass that Alma… ” in the printer’s manuscript and the 1830 edition. This phrase was removed from subsequent printed editions.