There have been Asian personal unions, though very rare. The most notable was King Chungseon of Shenyang and Korea. Then the Crown Prince of Korea, he was made King of Shenyang (today Liaoning Province) in 1307 by the new Yuan Emperor Kulug Khan for both contributions to the Empire (i.e. personal friendship with the Emperor), and because the region had become mostly Korean after the Yuan Dynasty evicted the Khitans and Jurchens. A year later in 1308, his father died and he assumed the throne of Korea as well, then a vassal of the Yuan Dynasty anyway. The personal union continued for the next 3 Kings and 44 years until King Chungjeong was deposed in 1351. The Kingdom of Korea went to his son King Gongmin and the Kingdom of Shenyang to King Gongmin's son, who adopted the Mongolian name Toghtua Bukha. When King Gongmin was assassinated in 1374, the Yuan Dynasty was being rapidly pushed north by the nascent Ming Dynasty. King Gongmin had only one legitimate son, Toghtua Bukha, but had named his illegitimate son, King U as King of Korea. A brief civil war ensued where Toghtua Bukha failed to claim the throne of Korea, and with the fall of the Yuan Dynasty the Kingdom of Shenyang was abolished.

I'll make another comment about why when I get off work.