Steven and Earl were unconsciously drawn to the Crystal Gems.
In canon, it is revealed that the corrupted gems were flocking to Beach City specifically because the Crystal Gems were drawing them there.Add this onto the Diamond's natural psychic connection to each other and, likely, Steven winding up at Beach City to meet the Crystal Gems was all orchestrated not by complete accident, but by gem instinct.
White finally grew curious enough to see what Pink saw in Earth.
Why else would she do this? In canon, White didn't seem to react much when it was revealed that Pink Diamond and Rose Quartz were the same person, meaning one of two things, either she didn't care about Pink or always knew about the masquerade and decided to play along. In the webcomic (and possibly the canon too to a lesser degree), it's possible for White at one point to ask herself what Pink saw in Earth, and it kept itching her till she decided to check it out herself, one thing led to another to lead to the event of the comic. How did White Diamond manage to not be noticed missing or of her recent inactivity (let alone questioned of strange activities if how and why she had Steven is any indication) for 14 to 15 years?
Per Word of God, that amount of time passing is pretty much the blink of an eye for beings that are The Ageless like Gems. In addition, White Diamond almost never left her quarters to begin with, so her being absent from Homeworld activity for over a decade and a half isn't eyebrow raising. It's just another day on Homeworld.