So, here's an Idea as to why the main timeline (Learning with Pibby in this case) and the Monument Mythos timeline are different.

682 used the Rabbit Miraculous.

Why?

To fix everything. He destroyed the constellation that makes Giza Glass, and destroyed all the special trees before George Washington was even born. He also made sure that every other major event in the Monument Mythos timeline never happened.

And then, what did he do?

Erased his memories. He couldn't bear never seeing his sister again, so he made sure to never remember her.

But that didn't erase his feeling something was wrong. Something was off. Someone wasn't here when they should be.

And that feeling tore him apart, causing him to hate humans. It also explains why he stopped after reuniting with Rosie again.

In each timeline, Rosie is always there. That was one of the things 682 forgot. But he knew it wouldn't be the Rosie he remembered.

And deep down, 682 still misses his old Rosie. But she's still there, ans she doesn't know it.

Every Rosie is a composite of all the timeline's other Rosie. Read: If a timeline's main branch gets destroyed, the new main timeline's Rosie will act like that Rosie, plus all the other previous Rosies. This even applies to the main (OWAR) timeline.

So yeah. Lizard did time travel shenanigans.