How did Neil know that Volkov is going to shoot the protagonist?

Final Neil's actions/perceptions are, from his inverted perspective, listed below.

From the perspective of TP/Ives/Volkov, the events below are listed in reverse-chronological order.

Offscreen:

1. Un-inverted Neil enters a turnstile and travels to the vicinity of the hypocentre.
2. Neil arrives after (from his inverted perspective) the un-explosion of the bomb. The gate is clearly closed (shown during a quick cut in the middle of the explosion, timestamp 2:17:31 on Youtube) and Neil is nowhere to be seen.
3. He arrives at the closed gate to find Ives and TP (moving in reverse) un-grabbing the algorithm + releasing the rope thrown down by Armored Car Neil. **edit
4. He unlocks and opens the gate. This occurs at some point during the exchange between Kat and Sator. **edit

Onscreen:

5. TP and Ives re-place the algorithm back in the dead-drop cylinder. Neil then witnesses Volkov reverse-emerge from being thrown down the hypocentre shaft (what a way to go eh). **edit

   **edit: Neil does not witness Volkov emerge from the shaft/any of the events after. He can be seen reverse-running away from the (closed) gate during the fight between TP and Volkov (his perception of events will move backwards from there). I've left them in the timeline to give a better idea of his actions in relation to the events as shown in the film.

6. TP un-shoots Volkov a couple of times with Ives gun (plot hole: why didn't TP just grab the gun and shoot him when his back was turned/Sator was chewing the scenery?).

7. Volkov un-drops his gun before being un-shot for the first time (in un-inverted time) by TP.

8. Volkov looks at Neil in (reverse?) confusion at the gate that, from Volkov's perspective, has just opened, but is about to close from Neil's.

9. Neil sees TP and Ives walk backwards through the gate.

10. Ives passes out.

11. Neil closes the gate, locking them out (from his perspective) but letting them in (from theirs).

12. Volkov is now not yet confused his timeline, and is reverse-pointing his gun at TP.

13. Neil, seeing this, makes a split second decision and bodily maneuvers himself in between TP and Volkov to protect TP from harm.

14. Volkov's gun sucks the bullet from wherever it's final resting place is (*sticking point: probably can't be in Neil's brain--be a helluva headache--has to be stuck in a wall, maybe his helmet, can't appear spontaneously because it's un-inverted) back through Neil's head, killing him.

15. Neil is dead. His body will eventually entropically erode/fade away.

16. Sator orders Volkov to shoot TP in the head.

*We can speculate that Neil's physical tissues, inverted as they are, can't exert enough force on the bullet to keep it from fully penetrating his body. This is implied (but not well defined) by the notion that inverted objects will "lose" to un-inverted ones.

Key Points

• Neil both opens and closes the gate. Whichever way you view the timeline, his actions provide a window of time during which the gate is open, allowing TP and Ives an opportunity to pass through it.
• When viewed from his perspective, I think we can conclude that Neil concluded (quickly, in the moment) that he had to catch the bullet to save TP.
• Had he waited to open the gate "earlier", he would be attempting to enter the tunnel out of phase with the temporal pincer movement, requiring him to take on Sator's private army's double-sided temporal defense by his lonesome.

There is a paradox going on here. We need to start from some assumptions to see it:

• Volkov's bullet and gun is not reversed, from Volkov's own perspective the bullet is shot out of his gun into Neil's head.

Let us look at the event from the forward perspective:

• TP and Ives get to the hypocenter, door is locked.
• Volkov reaches the hypocenter from another door to the left.
• Neils body is already on the floor
• Volkov shoots Ives
• Volkov goes to shoot TP and a forward bullet goes through a reversed Neil, Neil should have at this point a reversed wound

This is where the logic breaks, Neil from the forward perspective is now going backwards with a hole in his head, if we assume the mentioned assumptions. This would make it impossible for Neil to come to the rescue in the first place.

How do they make it work in the movie?

By braking the rules, what we see:

• Volkov reaches the hypocenter from another door to the left.
• Neils body is already on the floor, with blood on the helmet
• Volkov shoots and the blood disappears,
• Neil is seen moving backwards, uncanny to the whole thing

Now, the paradox:

From Neils perspective a bullet goes through him into Volkovs gun, still opening a hole in his head, that is why he dies. With Reversed bullets there is always a wound, moving forwards or backwards in time the wound is still there.

We see this with Kat, Kat is shot by an inverted bullet that goes through her, but she is still injured at the end. If both the bullet and her were moving in the same direction, then we would see, looking at the scene in the opposite direction that a bullet is going through her healing a wound in the process. But that is not the case. By the same logic, Neil would be both death moving forwards or backwards when the bullet goes through him, erasing his past and future, hence the paradox, does Neil exist or not?

How did Neil know that Volkov is going to shoot the protagonist?

He did not know that.

Neil's role in that sequence was just to open the door. In his timeline it meant to arrive when the door was open, go in and shut it. Then his head gets punctured by Volkov's bullet going back into the pistol, but that was just his bad luck and the Protagonist's good luck.

In normal timeline, the bullet path apparently was: Volkov's pistol, Neil's head, a part of the door (say Neil's head had bent the trajectory of the bullet which otherwise would still hit the Protagonist too), the floor or under it. Or the bullet could go near the Protagonist and past him into the corridor. In Neil's timeline it was obviously reversed.