Looking at Korean transcription rules for Japanese, I noticed that for some consonants, the hangul transcription would change if it was in the initial position:
カ /ka/ is transcribed 가 in the inital position, but 카 in medial of final positions. So the word カタカナ is transcribed 가타카나. ガ /ga/ is always transcribed as 가.
The same thing happens with /t/ and /tɕ/, so: タ /ta/ is 다 initally, but 타 medially and finally. So たれ (tare, "sauce") and だれ (dare, "who") are both transcribed 다레. The same happens with チ, 지 initially and 치 in other positions. The Korean Wikipedia article for ちょんまげ "chonmage", features both 촌마게 and 존마게 as a transcription.
Curiously, it does not happen with /p/, that is always transcribed as ㅍ.
This does not happen in the transcription rules for other languages, where seens to be /k/,/t/, tɕ/tʃ are consistently written as ㅋ,ㅌ,ㅊ even in the inital position:
English: cat 캣, time 타임, chart 차트.
Spanish: colcren 콜크렌, chicharra 치차라, tetraetro 테트라에트로.
Italian: Como 코모, Torino 토리노.
Portuguese: Cabral 카브랄, Coelho 코엘류, Tavira 타비라
So why Korean transcriptions of Japanese words uses the letters ㄱ,ㄷ,ㅈ for initial /k/, /t/, /tɕ/ while using ㅋ,ㅌ,ㅊ for other languages? What are the phonological or historical reasons for this different treatment when transcribing Japanese to Hangul specifically?
Edit: I think @jogloran explained well why ㄱ,ㄷ,ㅈ are used for the Japanese initial unvoiced stops and the article explains these and other transcription conventions in depth. The use of ㅋ,ㅌ,ㅊ for English initial unvoiced stops, that are more aspirated than the Japanese ones, is clear to me now too. But the question remains as why other languages that have initial stops with even less aspiration than their Japanese counterparts, such as Portuguese, use ㅋ,ㅌ,ㅊ in their official hangulizations.