It's alternate reality/parallel universes... there wasn't anything that caused the timeline split.
This.
Honestly, I think too much has been made of this "timeline split" since Fallout 3 came out. There is essentially one confirmed fact (above all others) that is relevant to this - and that's that in 2077, when the bombs dropped, the world looked a lot like the idealized techno-utopia popularized in old pulp comics, television, novels, etc. How we arrived at that end result is kind of besides the point. Fallout wasn't created as some hard science fiction attempt to logically determine the effects of a specific event. They simply thought it looked cool to have vacuum tubes and an Inkspots song for the opening credits. (Beyond events and trivia specifically set out and discovered in-game) there's really nothing more to it than that, and anything more is just rationalization on our part. (For example - I kind of prefer the view that culture went through it's normal cycles and simply arrived at a retro-retro style and mentality somewhere around 2077. Others feel comfortable with the idea that society stagnated for 120 years. But either way it's all rationalizations on our part, with no specific backing from in-game lore or canon.)
When Fallout 3 came out, they went a bit further with the iconic "retro" theme, than what you really had going in the previous games. (I'm rather fond of the move, myself.) And they felt the need to try and "explain" the situation to newcomers. But the fact remains that Fallout was designed with a specific style in mind and not a ton of thought went into "why" that was the case. So trying to hold it up to a different standard means it's obviously going to fall apart at the seams. Simply because it was never intended to hold up to rigorous scrutiny.
Frankly, there's no real reason there even has to be a "timeline split," beyond an obsessive need to justify vacuum tubes, black and white tv, and retro computer screens.