Does the intensity of a future event actually impinge on those experiencing premonitions?

This is very much the case. Premonitions happen because the person is sensing something of great significance to themselves, often because of an emotional reaction to it, and this will include things like accidents, serious illness, tragedies, losses, difficult circumstances with financial stress or relationship complications and disruptions, and so on, or a world-changing event of some kind that might affect the person indirectly but have huge significance for many, many people. So this is almost always the case that it will be an event with great meaning, and the premonition happens for that reason—there is an emotional reaction that needs one’s attention and the message gets through to conscious awareness to take heed.