This 決め決め (also written as キメキメ in katakana) is from 決める in the following sense:
Ichidan verb, Transitive verb
6. to dress up; to dress to kill; to dress to the nines
決める refers to neatly wearing attire such as a suit, uniform, costume or dress, or applying makeup suitable for some important occasion. It often refers to wearing formal attire, but depending on the situation, it can also apply to high-end clothes for a date, cute stage costumes, or even a Santa Claus outfit. 決まってるね means "You look sharp / put together!"
And 決め決め is a mimetic word that describes this. 決め決めの男性 alone could broadly apply to people who are always dressed like Instagram influencers or fashion magazines, but since it also has カチッと, I imagine mean who are dressed in formal attire or something like this.
カチッと is indeed an adverb, but 決め決め is a no-adjective here, and an adverb can modify a (no-)adjective, too. カチッと決め決めの男性 (adverb-adjective-noun) is structurally the same as とても面白い本.