This invention relates to a tire having a component of a rubber composition which contains a carbonaceous filler as a composite comprised of a disturbed crystalline structure which contains synthetic cubic (diamond) crystalline phase(s) combined with a significant amorphous phase content and which may also contain graphitic (hexagonal) crystalline phases. The crystalline phases are of a disturbed crystalline structure. The carbonaceous filler composite may therefore sometimes be referred to as a “disturbed crystalline/amorphous carbon material”. Such carbonaceous filler composite may be a product of, for example, an explosive detonation of a carbon-containing, oxygen-deficient explosive. Reinforcement of rubber compositions for components of tires is provided as a combination of such carbonaceous disturbed crystalline/amorphous carbon material together with rubber reinforcing carbon black aggregates and/or synthetic amorphous silica, and optionally with starch/plasticizer composite and/or short fibers. Such tire component may be, for example, a tire tread which contains a running surface for the tire.