The new movie unfortunately didn't explain it properly, but going into the time distortion just minutes later meant arriving years earlier in the future. That's why the genetically enhanced apes had arrived generations earlier despite Mark Wahlberg going into the singularity first.

At the end of the movie, Mark Wahlberg goes back to Earth, but the apes presumably followed him decades later, arriving hundreds of years earlier on Earth. That's why they could change history.