Thanks for the tag. Just, um…
Do you have a source for this? Or do you remember where you saw it? Because it makes some sense when I think about it, but I don’t think I can come up with 5 categories instantly. I’ve just got ‘noun + noun’ and ‘verb + noun’ or ‘noun/adjective + verb’ in my head for now. I usually think of 六書 when I hear ‘5-6’ and ‘kanji’, but those are kanji creation principles (which I don’t know all by heart anyway). It would be interesting to read more about the categories if someone else has already done such analysis. 
So, the answer is, at least in my experience… yeah, usually that’s exactly how it works. What comes first modifies what comes after. Why? Because that’s how modification works in most cases in both Chinese and Japanese. Both languages place their relative clauses before nouns, adjectives before nouns, adverbs before verbs etc. Are there exceptions? Definitely, but I can’t think of one now excluding the fact that 会社 and 社会 used to be equivalent. In the case of Chinese, there are also cases of compounds that mean almost the same thing whose grammatical class changes depending on which kanji comes first e.g. 適合 means ‘to suit’ (verb), whereas 合適 means ‘suitable’. Why? I suspect it’s because 合 is more common as a verb than 適.
Here’s the brief version of 栄光 vs 光栄:
https://community.wanikani.com/t/random-unconventional-mnemonics/49513/21?u=jonapedia
And the full breakdown I tried doing:
The irony of it all is this: my Chinese dictionary tells me that the two are equivalent in Chinese, just that one is more common in literary works. It also only lists 光栄 as a noun. However, online definitions are generally a bit looser, and usage examples, including one from the famous Ancient Chinese poet 李白, show that Chinese speakers also use 栄光 as a noun. I guess no one dictionary really has all the answers.
I’ve already covered 論理 and 理論 somewhere else on the forums:
事変 and 変事 are a new pair for me, though the first word seems to exist in Chinese. In Chinese, 事変 seems to have kept its literal meaning: it refers to changes (変) in matters (事) around oneself. However, it can also mean ‘incident’, because a major ‘change in events/matters’ is exactly what an incident is. 変事 apparently also exists in Chinese, but I think it’s a lot rarer. It tends to mean ‘incident’, just like 事変. To be honest, if you look both words up in a Japanese monolingual dictionary, you’ll notice that both have very similar first definitions. It’s just that 事変 has more specific definitions afterwards including ‘riot/unrest’ and ‘an outbreak of armed conflict without a declaration of war’. 変事 seems to be a more general word whose meaning is fairly literal: it’s a 変な事 – a strange matter/event, which is to say, an abnormal/extreme/extraordinary/unexpected occurrence.
I think one example of a Japanese compound in which the first kanji doesn’t clearly modify the second would be something like 子猫（こねこ). At the very least, it doesn’t seem to make much sense at first glance, because a kitten is obvious a 猫の子, and not the other way around. However, well… you could argue that it’s a ‘child cat’, even if that’s a little strange in English. The alternative is to remember that こ can also be written as 小 in compounds, which indicates that it tends to act like a sort of diminutive prefix, in which case the first element still does modify the second. I’ll just say that the habitual order in Chinese is 〜子, like in 女子 or 男子. 子 is often a diminutive suffix in that case in Chinese, but I’m not entirely sure why 女子 and 男子 tend to mean ‘woman’ and ‘man’ in Chinese… perhaps it’s because 子 is being taken in the ‘child=descendant’ sense, and everyone is someone’s child, so there’s no particular diminutive meaning: 子 probably just sticks around so there are two syllables to say instead of one, which is more natural in modern Chinese.