Problem lies with wounds that are non obvious. . .like those "behave normally then die in 6 rounds" crit results.
Note: I'm looking at this from the Healer profession spells. Are we talking about 'healing' in general, or the specific profession?
First of all, it depends on what you tell your player in terms of what kind of critical they just took. We have full disclosure.... maybe some of those injuries should be unknown to the player, but that's really just no fun in terms of six rounds later then saying "Oh, by the way... you fall over dead." Also, since we have Fate Points, the player needs to know if they need to spend a Fate Point. Even if you aren't going to tell them what the injury is, you do need to give them the opportunity to use their Fate Points, so at worst it will be "Um, you probably want to Fate Point that critical..."
Ok, so Transfer transfers
one injury from a target to the Healer. This implies the Healer needs to know what they are transferring. However, I believe there is no Lore spell for the Healer profession. So, where do you go from there? Basically, in my opinion, the Healer starts the to transfer the entire one injury without necessarily knowing how serious that injury was and then, during the transfer, learns how serious it was. Why? Because "Transfer" requires the Healer to expend as many power points as he would need to expend to fully heal that injury. So, if you need to stop bleeding, repair a tendon, and fix a broken bone, the "Transfer" costs the cumulative amount of power points as those three spells combined. Transferring can be expensive, and therefore I would rule that it imparts all knowledge needed about the injury.
As far as the whole subconscious issue; I'd say, subconscious injury, subconscious spell... it works. Now, at worst I'd let the Healer stop the spell from triggering automatically if he were conscious. At best I'd say the Healer has limited control over the subconscious spells.
Really, you have to decide if, in your game as a whole, subconscious spells are automatic if a player is unconscious or if you are going to allow some kind of control over them. We just automatically went with a limited amount of control over them simply because it sucks not being in control of your character.