Here "hand" represents power or control. The phrase "under the hand" is an idiom that means to be under someone's authority. Alternate translation: "were managers whom Konaniah and Shimei his brother supervised" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-idiom]])
Here "over" is an idiom that means to be in charge of. Alternate translation: "the official in charge of everyone who served in the house of God" (See: [[rc://en/ta/man/translate/figs-idiom]])