The Passover sacrifice in the Temple requires perfect organization, strict adherence to purity laws, and a clear division of labor between the priests and the Levites. During the service, everyone takes up a specific, designated position to carry out their defined tasks [ביאור שטיינזלץ]. A more specific approach suggests that this careful positioning applies directly to the Levites. They remain in their fixed locations and do not carry the sacrificial blood to the altar. Transporting the blood is a sacred duty exclusive to the priests, making the Levites outsiders for this specific task, in strict accordance with the Law of Moses [מצודת דוד].
Typically, the individuals bringing a sacrifice perform the slaughtering themselves. According to the Law of Moses, slaughtering is not a restricted task and can be done by any person. However, during this event, many of the people who arrive to offer their sacrifices are ritually impure. Because of this widespread impurity, the Levites must step in to slaughter the Passover offerings on behalf of the people [רש״י, רלב״ג].
Once the animal is slaughtered, the rules for handling the sacrifice shift significantly. From the moment the blood is collected in a vessel until it is splashed against the altar, the process becomes an exclusively priestly duty that cannot be transferred to anyone else [רש״י, רד״ק, ביאור שטיינזלץ]. In practice, the priests receive the blood and carry it to the altar. They then place the basins into the hands of the Levites to hold, keeping everything prepared for the priests to perform the final act of splashing the blood [מצודת דוד].