Newtypes don't just sense emotional intent and life, though. They also have precognition in general, like when Amuro sensed that the Solar Ray laser was about to be fired. No one died yet and he would have been too far away to sense the emotions, intent, or the presence of Gihren or the person who pushed the button to initiate the colony laser.
More examples might be Quess sensing 5th luna falling to earth and yelling out specific directions for the shuttle pilot to steer, even though she can't see the asteroid properly. Or Amuro and Char on foot inside Axis firing rockets and bazookas at each other, they can vaguely sense where the other person is, but they're also using tricks like remotely triggered rockets to try and kill each other with, yet they both keep missing. That implies that they know they can sense each other's intent and are deliberately trying to make it not so easy to sense where the attack is coming from by using tripwires and misdirection, but they both still manage to escape each blast.