Here's a bird from the 'cuckoo-shrike' family; it's Pericrocotus miniatus, from Sunda in Indonesia. The species name here, Minatus, is a reference to its color.
And this fine critter is a Vermillion Rockfish (Sebastes miniatus), another stunning example of Minatus. So I guess we all can agree 'miniate' is a sort of scarlet-vermillion bright orangey red, yeah?
The etymology isn't as surprising as slightly different place the etymology leads us. Minio is a word that came into Latin from some hill country tongue from Spain, there were lots of those back in the era when backwoods Latin was slowly turning into the various Romance languages we know today (French, Spanish, Italian, etc., etc.). Mino meant 'red lead' a mineral they were digging up in Spain which had an important use as a pigment, specifically in making a bright red ink that stayed nice and red over time instead of fading or just turning kind of brownish.
As the early Roman christian church spread its influence through establishing monasteries and by copying books, one finds that word minio leading not just to the word describing its color, miniatus, but also to a word that described the little pictures that ornamented the beautiful illuminated manuscripts that monks were making all over medieval Europe: 'miniatura.' Miniature -- the word isn't descended from the various Latin words that mean 'to make small', 'to diminish', like minus or minimum, it comes instead for this odd Iberian word for 'red lead.' Over time people began to associate the pictures more with their smallness and less with their redness, likely because they were more familiar with the 'mini-' words that meant small or lesser. But really, if we're gonna be specific, 'miniature poodle' shouldn't be the term for a small poodle, 'miniature' should indicate a bright red poodle.