1)
Why does it say "Al Yad Asaf"?
1.
Malbim: He taught Shir to them.
2)
Why does it say "ha'Niba Al Yedei ha'Melech"?
1.
Radak (1): The king appointed him to be the head in Shir and instruments, and wrote his words in his Sefer (Tehilim). Also about Yedusun it says "ha'Niba Al Hodos v'Hallel la'Shem" (3). Also Heiman was from Bnei Korach, and it says about him "Choze ha'Melech b'Divrei ha'Elokim Leharim Keren Yisrael" (5).
2.
Malbim: He said pleasant Shirim that the king composed.
