I think the OP is asking the actual mechanics of how a Primal does the tempering - from what little has been revealed, it appears to actually work on the person's soul - when the Primals like Ifrit and Garuda tried tempering the player (who has the Echo and is thus immune), both shouted something similar along the lines of "NO! YOUR SOUL ALREADY BELONGS TO ANOTHER?!!" - suggesting that the tempering process works by removing a person's 'soul' (or at least a part of it - specifically, free will, leaving them a mindless shell and from then on a thrall enslaved into the devotion and service of the Primal who tempered them).

If I remember rightly, a npc at Highbridge during the 'Attack on Highbridge' FATE there actually mentions that tempering strips a person of their soul and leaves them an empty husk, but I'm not 100% certain of that (it might be that the npc was just touting hearsay, and it actually doesn't work like that, but nothing is known with certainty.).