Rashi, quoting the gemora asks, “You might think that that specific Kohein is entitled to the whole meal offering himself. Therefore the verse says, 'To all of the children of Aharon it should be.' Consequently, you might think that it should belong to all of the Kohanim. Therefore, the verse says, 'To the Kohein who brings it.' How is [a reconciliation of these verses possible]?
The meal offering is divided to the family of Kohanim in charge of the service for that day. After all, Rabbeinu Bachya explains, “The Kohanim were divided into twenty-four group and would rotate on a weekly basis. As Yehoyada stated (our chapter, verse 9), “Each [captain] took his men, those who were arriving on the Shabbos and those who were leaving on the Shabbos, and came to Yehoyada the Kohein.”
Every one of these groups worked in the Bais Hamikdash from Shabbos to Shabbos. They were also sub-divided into groups for each of the six days of the work week. When Shabbos arrived, they worked together.
Thus, whenever a sacrifice was brought during their respective weeks of service, they would divide the sacrifice amongst those in that group who were working that day.