Jesus had been instructing the twelve, and now returns to addressing the whole congregation. It is doubtful that Jesus had separated the disciples in order to instruct them individually, so the congregation clearly saw, and heard, Jesus select and teach them as a group. In verse 1 he introduces them to the congregation as those who have been chosen to minister to them. Thus, the twelve were called, and in the presence of the congregation, presented as a group that was to be followed.
Even though the Nephites had been performing baptisms before, and with divine authority, Jesus appropriates baptism as an important ordinance of His doctrine. Thus, it might be the same action, but it has been placed into a new context. In that new context, that of the doctrine of the risen Christ, these twelve have been given public authority to baptize. They are also authorized to “baptize … with fire and with the Holy Ghost,” a feature not present (that we know of) in the previous Nephite baptisms.