I'm new to Korean, and it's possible I might have heard it wrong. But for BTS - I Need U and Forvo (pronunciation website), I hear "chakku". It doesn't seem to matter what precedes or follows the word, but it's always a "ch" sound instead of an expected "j" sound.
What you've found is right: unvoiced at the beginning of a word, otherwise voiced.
Then why “j” instead of “ch?” ― Romanization consistency for Koreans
And as to the title, that's because of the rigid romanization that wants a consonant to have the same romanization across words and sentences, irrespective of the actual pronunciation. You can find out the reason why in the writing below. The current romanization standard was standardized on July 7 of 2000.
Written in 2001 by Seh-joong Kim, the head of Department of Language Research, National Institute of Korean Language.
로마자 표기법이 개정되었다. 실로 16년 만의 일이다. …….
The romanization standard has been revised. It's been 16 years since the previous revision was established. …….
종전의 로마자 표기법의 또 하나의 문제점은 한국인들이 도저히 이해할 수 없는 표기법이라는 점이다. 유성음과 무성음은 한국인에게는 전혀 차이가 느껴지지 않는 변이음에 불과한 것인데 유성음이냐 무성음이냐에 따라 다른 로마자를 적도록 했으니 변이음을 구별해서 적는 것은 로마자 표기법의 기본에 어긋나는 것이었다. ‘부부’를 pubu로 적어야 한다고 아무리 가르쳐 주어도 왜 그렇게 적어야 하는지 한국인은 도무지 이해할 수 없다. 한국인이 이해할 수 없는 한국어의 로마자 표기법은 애당초 잘못된 것이었다.
Another drawback of the previous standard was that it didn't make much sense to Koreans. To them, the voiced and unvoiced sounds are just allophones, so having them have different romanizations is not a good way to go, considering what really “romanization” is for. It is a nonsense to them that “부부” should be written “pubu,” and a Korean romanization standard that Koreans themselves don't understand was a wrong decision to begin with.
But still, it sucks. Every Korean romanization method does. “어금니” goes “Eogeumni” and “내의령” goes “Naeuiryeong.” Supposing I have zero knowledge of the Korean language, how the heck am I supposed to read that out? You can see how messed up this is here, compared to Japanese or some other cutout languages for romanization. I can say this: Korean and Roman letters don't go well. Really, if you're to learn Korean, you need to throw that shit out. I'm not exaggerating.
A helpful note for you
“3 Reasons to Avoid Romanization When Learning Korean” by Learn Korean with GO! Billy Korean in YouTube.
I found this, which explains it, but I still don't know how to pronounce it. If someone can help me with that, that would be great.
Initial Consonant An initial consonant is any consonant at the beginning of a word. Initial consonants (especially at the beginning of sentences and phrases) are usually unvoiced. For example, the ㅈ in the word 저 ("I") is typically voiceless, especially as the first word of a sentence. That makes it sound more like "ch" than "j" to an English speaker. The consonants that follow this rule are ㄱ, ㄷ, ㅈ, and ㅂ. Thus, an initial ㄱ sounds more like "k" than "g", an initial ㄷ sounds more like "t" than "d" and an initial ㅈ sounds more like "ch" than "j". However, an initial ㅂ sounds more like "B" than "p":
가 ([ka]): initial sound is unvoiced. 다 ([ta]): initial sound is unvoiced. 바 ([ba]): initial sound is voiced. 자 ([ʨa], "cha"): initial sound is unvoiced.