The larger the agency, the more tools they have to actually sway public perception and 'decide' the Hero's powers and persona. They'd be able to do stuff like launch elaborate PVs to drum up hype, get their other talents to hint at the arrival of a new Hero, launch Origin movies in the theaters, and make their talent's debut into a spectacular affair with plenty of special effects to give the illusion that they've come into being with specific powers already possessed. If that roots itself strongly enough into public consciousness, then yeah, the Hero that the agency markets as a fire-breathing Hero will, in fact, gain fire-breathing powers.

Smaller agencies have less tools for doing that, so in the case where they're trying to market a fire-breathing Hero, perhaps instead the audience would latch onto other subjects involving that Hero. Maybe they misinterpret the shitty RL special effects and think that the Hero was releasing fireworks instead. Maybe they would misconstrue the fire-breathing and think instead that the Hero has magical sneezes. Maybe they wouldn't care about the fire-breathing at all, but rather they like the Hero's good looks, so they become a Fiery Romance Hero instead.

And, ofc, as public perception changes, so too would the Hero's power. So the fire-breathing Hero may have been just a fire-breathing person, but then maybe they made a cute 'rawr xd' expression that turned into a meme, and now there's tons of fanart of that hero being a dragon-boi, so voila, he starts developing draconic elements.