Created an account to say this, but there is a clear answer to this whole "reincarnation" thing.
The "reincarnated spirit" that Tharja/Shara is sensing isn't Robin or Mark or anything, it's the "Tactician's Spirit" that controls and guides each of these characters.
And that spirit is you, the player.
After all, what's the one thing each of these characters has in common?
They're all the self insert character.