The definition of -istic is:
Used to form adjectives from nouns, especially nouns in -ist and -ism, with the meaning "of or pertaining to" said nouns.
I don't see anything in there that could make words negative, but I can think of a few adjectives that are more negative with the suffix -istic. A few examples: negativistic, simplistic, moralistic, and legalistic.
Best Answer
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
simplistic: "simplist" + ic: being like someone who
moralistic: "moralist" + ic: being like someone who is
legalistic: "legalist" + ic: being like someone who is
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.