Short answer: it's not the "istic", it's the underlying "ist", or ultimately ism.
Let's examine your four examples:
negativistic: "negativist" + ic: being like someone who
has a tendency to be unconstructively critical
simplistic: "simplist" + ic: being like someone who
"studies simples", which are "herbs used in healing, medicine of one ingredient only; the notion being that each herb possesses a particular virtue, thus a `simple' remedy", thus a simplist is a person who subscribes to a theory which is over-simple, trying to explain too much by a single principle
moralistic: "moralist" + ic: being like someone who is
given to moralizing, which (in the perjorative) is "indulgence in moral pronouncements; the exposition (often superficially) of a particular moral code"
legalistic: "legalist" + ic: being like someone who is
like a goddamn lawyer
So each of these words, rather than directly ascribing a quality, is defining the trait in terms of acting like an a -ist. This is not obvious at first blush, because the -ist has been subsumed into the -istic, sometimes to the extent that modern English doesn't even have original -ist (or -ism) any longer, as in simplism and simplist. But none the less, in each case, the etymology traces back to a form of "X-ist" + "ic": "acting like or having the quality of an X-ist".
So to the extent -ist s and -ism s often have negative, pejorative connotations, so do -istic s. But while ists and isms as a class are charged with obdurate or doctrinaire (and often supercilious) qualities, whether particular ists and isms -- and by extension, istics -- do, depends on society's perception of that particular doctrine.
Consider the range of senses in altru-istic (positive: one who practices altru-ism), sad-istic (negative: one who follows de Sade), art-istic (neutral/descriptive or positive), unart-istic (neutral/descriptive or negative), character-istic (not even applicable, because it doesn't derive from an ism), bolshev-istic (positive in Soviet Russia, negative in McCarthyist America). The overtones come from (society's perception of) the root ism in each word.
It does seem that your proposition is by and large correct. One can think of a variety of exceptions, but it generally seems to hold that where you find an ...ism, there will usually be an ...ist!
But not all followers of something are ...ists, some are ...ites e.g Luddites (I've never heard Luddism used, though).
Adherents of Nazism are plain Nazis. That is a clear exception of an ...ism, without an ...ist. I have no doubt that there are others and people will think of them.
In British politics you have had, at different times Benthamites, Brownites, Blairites, Bennites etc. But I am not sure if any were ...isms.
Of course it doesn't work the other way round. There are many ...ists who do not follow an ...ism e.g. economist, sociologist etc.
Best Answer
Crucify originally had a distinct etymology from the others
Crucify comes from Latin crucifīgō with the present infinitive crucifīgere and the supine crucifixum. It means "to fix to a cross" not "to make into a cross". It ends in -fy in English because we got it through French; the OED says more specifically that it is from "Old French crucifier (12th cent.) = Provençal and Spanish crucificar, repr. a late popular Latin type *crucificāre instead of Latin cruci fīgĕre to fasten to the cross, subseq. as one word crucifīgere." Although this verb came to have the same ending as the other verbs you mention, it didn't originally, and the noun crucifixion remains faithful to its origins.
The verb suffix -ify comes from Latin verbs that had -ificat- forms
The English verb suffix -ify (which is moderately productive: you can see an overview of the tendencies for new formations at What is the difference between the suffixes -ize and -ify? and Suffixes for verbification: -ify, -icise, -ificate) comes from Latin verbs ending in -ificō, an ending derived from a reduced form of the verb faciō "make". Latin verbs ending in -ificō belonged to the first conjugation and so had present infinitives ending in -ificāre and past supines ending in -ificātum, with the thematic vowel A.
Some potential -ification nouns are "blocked" by other nouns
Testify seems to be from Latin testificor which basically just conjugates like the passive form of an -ificō verb, as it is a first-conjugation deponent verb. It has the participle form testificatum.
The word "testification" exists in English, it's just very uncommon. A well-established preexisting noun related to a verb will usually be preferred over a more complicated noun derived from the verb that would have the same meaning; this is called "blocking", and there are other examples like how *terrification and *horrification are very rarely used compared to terror and horror. Aside from blocking by testimony, another thing that might play a role in the low frequency of "testification" is that the meaning of the suffix -ify seems to be somewhat more opaque in testify than it is in some other words ending in -ify.
The -(i)faction nouns are based on the conjugation of Latin faciō
Satisfy comes from Latin satisfaciō, which conjugated like faciō in Latin as a third-conjugation verb without vowel reduction. The present infinitive was satisfacere and the supine was satisfactum.
There are a number of nouns aside from satisfaction that end in -(i)faction and are related to verbs ending in -(i)fy. See the results for *ifaction on OneLook Dictionary Search. One example is putrefaction (corresponding to the verb putrefy), which seems to be much more common than putrefication. Some other examples are petrifaction (corresponding to the verb petrify) and liquefaction (corresponding to the verb liquefy).