First and foremost, I think it's very dangerous to try to approximate Mandarin sounds with parts of English words, partly because we all pronounce English slightly differently and partly because some sounds just don't exist in English. There is no "ü" [y] in English, so trying to use English here will just trap students and never really allow them to learn the sound.
In order to straighten out pronunciation in the case of "j/q/x + u", we need to first look at basic spelling rules in Pinyin. There are two distinct vowel sounds in Mandarin spelt "u" and "ü". The are very different, although they look similar and are mispronounced by a large number of English native speakers. The first is a close back rounded vowel, the second is close front rounded vowel. Don't think of "ü" as being anywhere close to "u" because it isn't.
The problem (for learners) is that the dots are only written when there is ambiguity, which is only the case for "lü" and "nü" since "lu" and "nu" also exist in Mandarin. In all other cases, the dots have been removed and we just write "u". This happens for all syllables starting with j/q/x, so "ju" is really "jü", "quan" is really "qüan" and "xue" is really "xüe". There are no "lün", "zhün" or "chüan" and any such pronunciation is definitely not standard.
So, to answer your question, the "u" after j/q/x (and in "yu", "yun) should be "ü" and is pronounced completely different from a normal "u". In IPA, this sounds is written [y] or perhaps more accurately as [ɥ] in glides. When it occurs after other initials, it's a normal "u", which is written in many different ways in IPA depending whom you're asking, but [u] and [ʊ] are the most common.
These two sounds never overlap, they are in what's called complementary distribution. If you start mixing them, the risk of being misunderstood increases a lot. In fact, if you get these finals right, you can get away with other pronunciation oddities, such as mixing zh/ch/sh with j/q/x (which is common) since the former can only be followed by "u" and the latter only by "ü", listeners will still know what you're trying to say even if you pronounce e.g. "zh" and "j" the same way.
While I'm at it, I should also mention that all "un" that aren't preceded by j/q/x are actually "uen", which makes the pronunciation even more distinct from jun/qun/xun. How pronounced that "e" is depends on the syllable, the tone and the speaker. It seems to be most prominent for third tones where it's very easy to hear and least prominent in fourth tones.
Regarding different dialects or regional accents, I'm afraid someone else will have to step in. What I have written above is the standard, but there might be places where people don't pronounce things like that. However, I've lived in Taiwan for many years and have spoken with lots of people from Beijing and I have not observed the north/south difference you mention. Take this as a personal observation, I haven't done much research into locally accented Mandarin (except the Taiwanese variety, which isn't relevant here).