In Tenet, when someone got shot by an inverted bullet, shouldn't the person be hurt before getting shot and recover immediately after the inverted bullet shoots him? If not, then why was the wall recovered immediately after being shot, but humans are not?
I struggled with this as it seemed to be a temporal loophole but I think there is an answer - which lies at the end if you don't care for the details.
Examining the relevant scenes of the film, this is what seems to be happening.
Regular - We see regular Kat being dragged into the see-through room while a bullethole is on the separating glass. Inverse Sator catches the bullet with his gun from the glass and the bullet passes through Kat's body and into the chamber of his gun. So now Kat is inversely shot and will soon die as her current regular timeline moves foreward. After this, inverse Sator walks backwards through the turnstile as she is bleeding.
Inverse - We see Sator entering Kat's room right after he inversed his timeline - exactly as the regular timeline above just ended. He finds Kat already wounded on the chair. There is not bullet hole in the glass because the shooting has not happened yet in the inverted timeline (which we are now in), nevertheless Kat is wounded because this is the future of her regular timeline. He picks her up, pulls the trigger, the bullethole appears on the glass and Kat is HEALED. He takes her in the car and the car pursuit unfolds with Kat being perfectly healthy in the car as we see her. Remember, this is Kat's past we are moving through now, this is why she is not bleeding. For Kat, this is happening before she got shot in the glass room.
- Regular - The Protagonist stabs the inverse Protagonist in the arm.
- Inverse - The inverse Protagonist starts feeling pain in his arm as they move inversely through time towards the Freeport in Oslo. Right before entering the Freeport, the wound is open and bleeding - so as he moves inversely towards the stabbing, his wound get worse. Then he enters the Freeport, the fight with his regular self occurs, and when the regular Protagonist stabs his already bleeding arm, the wound heals! (we don't explicitly see that one, but when he gets out through the other side there is no more mention of the wound and furthermore it logically follows from what has happened until now)
So, the answer is yes, a person is hurt before getting inversely shot and recovers immediately after the inverted bullet shoots him. This is consistent with the bullet holes also.
It's a mindbender, but this seems to be the answer. When you shoot someone, either regularly or inversely, you injure him for his own future. He will keep bleeding as his his own timeline moves on to its future. But in your, opposite, timeline the things you will experience are what led that person there on the first place. He deterministically needs to arrive there for the shooting to happen.
I'll say that again as is it the key. When you shoot someone, either regularly or inversely, you injure them for their own future. Your future is their past, in which they were sill alive.