The simplest answer is: it isn't wholly separate. It only diverged from our own timeline when G'raha altered the events of "his timeline's" past to the point that those events couldn't come to pass any more. A new branch of time forms to hold this new future, and now is of equal importance as the original.
Prior to Shadowbringers there is one timeline. Afterwards there are two. The timeline is a Y shape.
When we travel to Elpis, we move from our "branch" of the split timeline to the "trunk" that is shared by both halves of the split. Thus our actions there affect both timelines.
Unfortunately there's no satisfactory answer as to how the time loop formed, but it did, and things have just always happened that way. All the parts interconnect neatly.
Also, just in case you're working under what seems to be a common misconception: the First is not a "timeline" separate to the Source, it is a "shard" and still aetherically connected to the Source. A copy of all the shards exists in each half of the split timeline, with the other timeline ruined because of the First's rejoining.
