Actually, Millar reinvented the Avengers by using a cinematic narrative style, instead of the classic comic book style, but it was just a creative thing. Back in 2002, nobody actually thought that the Avengers would be actual cinematic material. The MCU would not be started until years later, and even then the initial brainstorming (before settling for the Phase 1 films) suggested properties with little or no relation to the Ultimate line, such as Ant-Man, Shang-Chi, Luke Cage, Runaways (if I remember fine), etc.
That didn't happen from out of the blue. Bendis first wrote "Ultimate Spider-Man", a comic set in an alternate universe, so if he failed (as Chapter One failed before it) it would have been canceled and nobody would had noticed. But it did not fail, and instead it outsold the main Spider-Man comics. So yes, of course that he was promoted to write the mainstream universe comics as well. But "hot"... the Avengers were not "hot" back then, they were a cult classic at best, a minor and irrelevant comic at worst (just check if Chuck Austen's Avengers were "hot"). It was Millar with the Ultimates and Bendis with his run, who made the Avengers hot. Then the film based on the Ultimates made the Avengers real-world hot, and the rest, as they say, is history.