The system of land inheritance in Israel required the tribes to set aside dedicated cities from their own territories for the tribe of Levi. Once the priests received their designated locations, the distribution process shifted to the rest of the Levite families.
The descendants of Kohath who were not part of Aaron's priestly line needed their own allocation, as Aaron's family had already been given cities within the lands of Judah and Simeon. This remaining group of Kohathites consisted of the descendants of Moses, Izhar, Hebron, and Uzziel [רש״י, מצודת דוד]. To accommodate them, ten cities were drawn by lot from the territories of Ephraim, Dan, and the half-tribe of Manasseh. The inclusion of the half-tribe of Manasseh specifically refers to the portion of the tribe that settled west of the Jordan River, within the borders of Canaan [ביאור שטיינזלץ].
Gathering these cities from across different tribal lands was a deliberate process. It fulfilled the earlier command that each tribe must contribute cities to the Levites in direct proportion to the size of its own inheritance. A larger territory required giving more cities, while a smaller territory required giving fewer [רש״י].