Being jealous is what's called a free adjunct. It would be very difficult to explain exactly what linguists understand about it to you, since it requires a lot of technical knowledge.
The best way to explain it is this. Let's start with the sentence:
Mona didn't let her boyfriend dance with any of the cheerleaders.
At this point, the listeners doesn't know why Mona didn't let her boyfriend dance with any of the cheerleaders. However, the speaker wants to let the listener know why Mona didn't let him, so they want to add that Mona was jealous.
The most straight-forward solution would be your sentence,
Mona didn't let her boyfriend dance with any of the cheerleaders because she was jealous.
The reverse also works (Because...Mona...). But they require two clauses inside the main sentence.
[[Mona didn't let her boyfriend dance with any of the cheerleaders] [because she was jealous.]]
Instead of having to put two clauses inside the main sentence, why not just have one with some extra information tacked on?
[Being jealous,] [[Mona didn't let her boyfriend dance with any of the cheerleaders.]]
This is analogous to:
Jealously, Mona didn't let her boyfriend dance with any of the cheerleaders.
The difference is that with jealously, it moved from the main clause to outside it. In other words, the original sentence was:
Mona jealously didn't let her boyfriend dance with any of the cheerleaders.
And then the jealously moved in a process we call topicalization. Topicalization in English moves parts of the sentence to the front so they're more prominent.
↓----------¬
Mona jealously didn't let her boyfriend dance with any of the cheerleaders.
With being jealous, however, it didn't move from anywhere. The speaker just thought of it and attached it to a point where it's allowed, which includes the front of the sentence.
Being jealous
↓
Mona didn't let her boyfriend dance with any of the cheerleaders.
In conclusion, being jealous is basically a quick way of saying "Mona was jealous, therefore...." with fewer words.
I think what the page meant by saying "when, where, who" is that the perfect form doesn't go well with expressions suggests a particular time. The example sentences given at the linked page seem to be all about it.
The default past tense is the simple past, as Michael Swan says in his Practical English Usage (§421.4 "In general, the simple past tense is the ‘normal’ one for talking about the past; we use it if we do not have a special reason for using one of the other tenses.")
The perfect forms are needed basically to add the sense of completion to non-finite verbs such as infinitives, participles, and modal verbs. Because such tool exists, it's also used to talk about past events, but it ends up saying 'up until now' ('up until sometime ago' when it's the past perfect). Because it's tenseless by itself, it makes the sense of time vague, thus it has the sense of duration at the same time it conveys the sense of completion.
The use of the perfect forms are more to do with meaning than tense. Grammar books usually says it's one of tense form, but actually it's not about tense. Linguists call it 'aspect'.
The perfect form goes well with expressions like already, recently, just, since, ever, never. But it doesn't go well with expressions of particular point of time, when, such as yesterday.
I've read something more relevant to the OP's question, in the same M. Swan's PEU:
§457.1 (...) we usually prefer a past tense when we identify the person, thing or circumstances responsible for a present situation (because we are thinking about the past cause, not the present result). Compare:
Look what John's given me! (thinking about the gift)
Who gave you that? (thinking about the past action of giving)
Also
PEU §456.5
We normally use the present perfect to announce news. But when we give more details, we usually change to a past tense.
There has been a plane crash near Bristol. Witnesses say that there was an explosion as the aircraft was taking off, ...
Best Answer
The rule you are referring to ("no will" with when) only applies in those sentences in which when introduces a time clause, e.g.:
In your example, when introduces a sort of reported speech, it is not a time clause. It is as if it were derived from direct speech along the lines of:
Therefore, it is correct to join the two sentences as: