Sforno on Numbers 5:10/ספורנו על במדבר ה׳:י׳

1ואיש את קדשיו לו יהיו, however other kinds of “holy” gifts, namely ordinary tithes and trumot, may be given by the owner to whichever Levite or priest he chooses, not necessarily the priest officiating in the Temple at the time the gift is presented.

2איש אשר יתן לכהן, once the owner has given “his” holy portion to the priest it becomes secular, mundane, not encumbered with any restrictions. Rather, לו יהיה, it is exclusively “his,” neither the previous owners nor other priests can legally deprive him of it.