What are the Cantonese to English transliterations for 俊傑, 俊熙, 俊健, and 俊文? I found zeon3 for 俊. That does not sound right.
/zeon3/ is a Jyutping. which is not meant to be written as English words
According to Cantonese to English Translator
The four names 俊傑, 俊熙, 俊健, and 俊文 are transliterated as Joon Jae, Joon Hee, Joon Kin, Joon Man
My Hong Kong-born nephew's name contains the word 俊 So I know it is written as Chun
The Hong Kong transliteration of 俊傑, 俊熙, 俊健, and 俊文 would be Chun Kit, Chun Hei, Chun Kin, and Chun Man
I just look up famous Hong Kong people whose names contain these Characters and read their Wiki profiles
For Mandarin transliteration, just use Google Translate
Result: Junjie, Junxi, Junjian, and Junwen
To use "standard" transliteration that I've commonly encountered it would be: Chun Chieh, Chun Hei, Chun Jian, and Chun Wen. The zeon is based on jyutping, one if the cantonese equivalents to pinyin.
I put standard in quotes because while it is commonly seen and familiar, Cantonese transliteration is more of something established without a standard. This is why Tang Ho found different versions when looking up people with similar names.
To this day, you will often see completely different pronounciations all transliterated into the same letters, such as Shi (si, sek, and sat being jyutping examples) or Kai (hoi and kai).
Sometimes, this is because the transliterator just ignores the Cantonese pronounciation and transliterates directly based on what Mandarin would be. When you consider that the point of transliteration is to be understood by those who don't know the source language, it can be understandable why using more familiar versions are useful. Regardless of agreeing with the sentiment, it is a part of why this happens.
Another huge factor is that many of the transliterations are very old, from the 1800s or even further back. In these cases there is the usual issue of no transliteration being accurate to the source language's sound, combined with pronounciation changing over time. A famous example is MK aka Mong Kok, Hong Kong (wong gok, hoeng gong). I mention the two letter abbreviation since this not accurate transliteration is used in Cantonese speech frequently, really showing how established these are.
These phenomenon are the reasons the jyutping zeon looks so different from what you see in transliteration. Differences between an accurate attempt transcribing the sound and regular transliteration is not unique to Cantonese either. A famous Mandarin example is Peking. Few people would realize it is the same word as the modern and more accurate Beijing if they didn't have any Chinese knowledge.
P.S. in your image the machine translator has transcribed the names into Korean transliteration. This is just an error of the machine and not related to any normal transliteration.
There's a Chinese University Hong Kong website that you can use as a reference
俊 is listed as zeon3