Why "present simple" and not "simple present"?

I don't think "present simple" or "past simple" contradict the "adjective noun" ordering rule;

You can consider "present" and "past" (the two morphologically distinct tense forms of the English tense system) as qualifying grammatical aspects (progressive or perfect).
Hence "past simple" or "present continuous".

But it is more a usage than a strict grammatical rule here:
Present simple can also be referred as "Simple Present".

To rephrase the first part (about adjectives) a bit more clearly:

The English Grammatical aspect Wikipedia entry mentions:
"The English tense-aspect system has two tenses, present and past, which are morphologically distinct."

My point is that the tenses act as qualifier (like adjectives do) for the grammatical aspects (same wikipedia entry: aspects beings "simple", "progressive", "perfect", ...).

So if the tenses are considered as adjectives, they are rightly placed in front of the aspects they qualify.

My guess as to why there is variation is because Latin was the original language of education (among European languages). In Latin, it would be natural to use the order "present simple". With formal descriptions of English grammar that came later, some people translated these terms literally into English, retaining Latin word order, while others preferred to translate in a way that follows standard English order (as VonC said, both orders are used in English). Also agreeing with VonC, I don't think it truly violates adjective noun ordering, only because it has crystalized as a set phrase — like an idiom. People use the "present simple" order because it is (one version of) the name of this term.

I don't have a source on the history of Latin grammarians and their influence on English grammarians, so that is why I say it is a "guess", but if anyone does have a source, do let me know!

My guess would be that the reason "Present" was put before "Simple" is because that's the main concept, which is further extended by the adjectives "simple", "progressive" and "perfect". It's also easier to organize mentally as categories of tenses:

Present simple
Present progressive
Present perfect

Past simple
Past progressive
Past perfect

Someone then would naturally tend to see them as the 3 different forms of the "Present" tense, instead of the 3 different tenses of the "Simple" form as below:

Simple present
Simple past
Simple future

Progressive present
Progressive past
Progressive future

The latter doesn't emphasize the main categories which should be the tenses.