The Korean separation of 설음 (coronals, literally 'tongue sound') and 치음 (affricates and sibilants, literally 'teeth sound') can be seen in the companion to the 훈민정음 (訓民正音, Hunminjeong'eum), the 동국정운 (東國正韻, Dongguk Jeong'un) from the 1440s.
But this split of the 설음 from the 치음 is already found in Chinese 韻書 'rime dictionaries', including the 韻鏡 Yùnjìng from the year 1161 (Song dynasty). This is part of the "36 initials", where the dental stop series (舌頭音 shétóuyīn) 端透定泥 and the palatal/retroflex series (舌上音 shéshàngyīn) 知徹澄娘 are both called 舌音 and listed under the pentatonic note name 徵 (zhǐ), whereas the dental affricate-sibilant (齒頭音 chǐtóuyīn) series 精清從心邪 and palatal/retroflex affricate-sibilant (正齒音 zhèngchǐyīn) series 照穿牀審禪 are in 齒音 and under the pentatonic note name 商 (shāng).
The concept of the initials of Chinese (in their order) is attested earlier, from the Tang dynasty, from a manuscript by the Buddhist monk 守温 Shǒuwēn. The 30 initials there also show the distinction between coronal stops and affricates/sibilants, but with 心 and 邪 placed under 喉音 (hóuyīn) rather than 齒音. This has parallels with ungrouped (अवर्ग avárga) consonants in the phonology of Indic languages, not surprising considering the Buddhist nature of these manuscripts.
But upon comparison with the Sanskrit वर्ग (várga) system, we see that this distinction arose very much within the Chinese phonological tradition. As stated by Jacques 2017 in the Encyclopedia of Chinese Language and Linguistics:
An indirect Indic origin for the rhyme tables is probable, but in any case the
Chinese scholar who established the rhyme table tradition and its terminology did
not slavishly translate the Sanskrit terms, but rather invented a new framework
inspired by them.