I compared successive timelines to the pages of a book but this comparison is incomplete. When reading a book, we can turn the pages either way and can reread earlier pages. The pages coexist. They are spatially, not temporally, related to each other.
In the Time Patrol series, the timelines are temporally related. They are before and after each other and are causally related. A time traveler leaving timeline 1 generates timeline 2. Thus, when attention is on timeline 2, it cannot return to timeline 1 except by remembering that timeline and conscious beings whose existence is confined to timeline 2 have no way of remembering timeline 1.
It follows that two temporal dimensions are involved. To stay with the analogy of the book, the horizontal dimension of each page represents the familiar temporal dimension that each of us experiences from birth to death, that I am experiencing now as I cause words to appear on the screen and that you experience when you read the words successively. The process of turning the pages - in this case, it can be in one direction only - represents a second temporal dimension experienced only by time travelers who pass between timelines.
In the second temporal dimension, a time traveler who has arrived in timeline 2 says that timeline 1 no longer exists but this does not alter the fact that the people whose world lines existed in timeline 1 did experience their lives from birth to death. After someone has died, we do not say that he did not exist and there is no reason to say this from the perspective of a subsequent timeline. Within timeline 2, i.e., on a single page of the book, it is true to say that an inhabitant of timeline 1 has never existed. We are used to thinking of events as occurring only within a single temporal dimension so confusion is caused by trying to think of two temporal dimensions simultaneously.