Latin is the language used by wizards and witches in the Western World when they cast spells. Latin is Indo-European - a language family that doesn't include pan-Asian/tonal tongues.
So what languages did wizards use to cast spells in Asia?
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There are very few references to wizards in Asia or from Asian countries in the Harry Potter books themselves. Quidditch Through the Ages mentions that Quidditch isn't as popular in Asian countries where flying carpets are the main form of travel instead of brooms, and mentioned that countries like India, Pakistan, Bangladesh, Iran and Mongolia all have their own Ministries of Magic. Also of note, Quidditch is more popular in Japan, and Japan has its own Quidditch teams, the most successful of which is the Toyohashi Tengu.
The most detailed information given anywhere in Harry Potter about Oriental magic or wizards is in the Pottermore writing on the Japanese wizarding school, Mahoutokoro. Nowhere in that writing is it mentioned what language they use to cast spells.