the junction was an event that happened initially around 8 months ago, caused by a fight between two chaos lords : child and klarion.
muses from dc's side would remember the chaos that rendered their world incapable of supporting life --- to the extent that their earth was split in half in the hours before --- while muses from bnha would remember the dread that came hours before the initial event; there was a flash of light, and then everything was 'mixed up'; every muse would've been affected in the sense that they would've been confused for hours to the extent that most couldn't even walk, much less stand.
in the next few days it would've been found that more things are more odd. U.A high, a hero school from japan, was placed in america instead of it's origin. While the watchtower for the justice league is farther acrossed the globe than it's original point.
in the next coming months, bnha's government became more of a standing point --- taking over where there wasn't many laws in the first place in dc --- muses would find that it's illegal to use a quirk or powers in public when you're not licensed to do so / a hero in the governments eyes, and thus dc's heroes would be strongly recommended to take a test offered by their countries hero commission or else people in bnha's world would simply see them as a vigilante, or a villain outright.
in the next coming months, muses will experience the oddities of exploring a world that's two-in-one. they will experience the world glitching around them, 'rewriting' their surroundings.