There's nothing in the lore that suggests that souls have any sort of true connection to their relative shards; on the contrary, there are numerous instances of souls of the dead playing by the rules of the shard they are in and needing explicit labor to be ferried between them. To name just one example, the soul of Minfilia is explicitly ferried from the First to the Source by Hydaelyn.
I don't think we have a definitive answer to this. Though we could easily learn the answer if something unfortunate happened to the Rowena or Gerolt in Solution 9. Y'know, for science!
My guess would be that there isn't anything particularly special happening during a Rejoining, that everything in the shard dies and simply gets deposited into the Source. If that's the case, it would mean that the souls of the dead have some manner of magnetism to their counterparts (living or dead) and fuse with them. The demonstrated exception to this rule would be souls that are "undead" like Ardbert; he's technically dead, but in a way that has resisted the natural process of what happens to souls after death.
(I wonder what this means for the Scions who spent years in the First? Y'sthola would have noticed if their souls had become more dense, suggesting they didn't join with their counterparts. Does that means that they have living counterparts somewhere on the First? Or that the rules work differently for the type of out-of-body experience the Scions were having? It will be interesting to see whether whatever explanation the writers eventually provide is internally consistent.)
