Jesus instructs the twelve that this sacrament was something that should be repeated: “this shall ye always do to those who repent and are baptized.” Although that might indicate that it was to be done prior to baptism, modern readers understand that this is an oft-repeated event to renew the covenants we made at the time of our baptism.
The Nephite people had been familiar with the concept of a church as a gathering of believers inside a society that also included non-believers. The people gathered at Bountiful were certainly all believers now, even if there might have been some who were not believers before.