[Extremely Slight Spoiler Warning for both OoT and MM]
There is something that sort of explained the 3rd split for me. Someone posted it on the forums and I am sorry that I can't find the thread right now, but it made a lot of sense. Within the game, there are three stories, the child (before the master sword), the adult, and the child (the well and the spirit temple). The third split in this theoretical case is the second child timeline. Adult Link escaped the adult timeline, but the events still happened, and that means the child link can escape that smaller child story timeline and the events will still happen, but because it is in the past, there will be different consequences. Link does not defeat Ganon in that timeline because he is no longer part of that timeline. It doesn't entirely make sense with the popular idea of time travel, because Link disappears, but he already does that in the adult timeline, so there is nothing stopping him from doing that in the secondary child timeline. This doesn't explain Ganon gaining the full triforce (unless the Gods/Goddesses gave the triforce pieces to the correct people later in life for some really strange reason, but that's for another forum thread I suppose), but it does explain how a third split would be able to happen, which I think was Nintendo's main point, as there are a lot of little quirks that make the timeline technically impossible anyways.
Majora's mask has timeline splits as well, but those splits all lead to the end of Termina, so nothing can really happen after that. There is only one split that is successful and that is when link is successful.
I highly doubt this was Nintendo's intention for the timeline originally, but when they were pressured in working on a timeline they decided to find something that would kind of work and it actually worked decently well.