As we see in the events of the Incredibles, the United States wnet to a transformation at some point of it's history (probably near the 70's or 80's considering the extra material Colectors Edition DVD and the own ``Glory Days´´) that we see Mr. Incredible, Elastic Girl and Frozone in their adventures in a 80's like city, the rest of the movie probably sets in the late 90's/early 2000's based on some of the computer technologies, cars and architecture.
Probably in this universe the heroes just became popular at the late 70's but were used by the military in secret missions at the 50's and 60's, mainly due to radiation experiments of the Cold War era, the same radiation that created monsters in Japan and affected not only animals but also people and making a huge upgrade in the twentieth century's science.
Naturally, regular people and animals were submitted to radiation that changed how their bodies worked, creating super beings with powers never known to man before the World War II. This explains the number of villains and heroes who are growing more into becoming world's dominant population.
Probably at those ``Glory Days´´, the events that left superheroes illegal in America were a watershed in worlds politics and many nations followed the american decisions, and other part of the world followed Japan on not making fighting crime a offense on the law mainly because of their monster attacks who increases day after day.
Since the events on the One Punch Man series seems to happen at the 2010's due to japanese technology on cell phones and LCD televisions that we can see at the manga, it's secure to say the niponic superheroes have way more approval than the americans who work in secret in private or governamental missions, that way alien civilizations like the one who attacks the Hero Association at Japan have way more chances on attacking the planet since their science can create such strong creatures like Saitama, although in that case it were probably his hidden powers manifestating due the training he had.
In that way, I'm can theorize that in this reality both universes have the same chance of co-exist.
P.S. Pardon me for my bad grammar, I'm not a english speaker.