Each time travel story has its own set of rules. Sometimes, one of the rules is something along the lines of 'do not to let a former self see your older self' (a la Back to the Future). Other times this isn't a problem. For instance in The Time Traveler's Wife time traveler Henry DeTramble not only meets former selves, he mentors them, lets them know what is about to happen, and even engages in circle jerks with them. He is aware that what will be will be, and he cannot change his fate. The unnamed traveler in Ferrell's book not only meets his other selves he actively works to change their fates, and thereby "untethers" himself from many of the selves he meets at the annual convention he arranges for himself on his birthday. His desire to save himself from the pain of a broken nose results in various parallel life trajectories, and alternate realities (again refer to Back to the Future movies for more of how this happens) with some disastrous results. One good thing that happens as the result of all of this, however, is that our Time Traveler finds work at the New York Public Library of the future (year 2071), where our hero literally works for food, an irony that was not lost on this librarian.
The narrator's job is in the "book exchange" where the workers search for books and send them to "those who need them." The books are placed in precariously high stacks and when the narrator asks how they find the randomly placed books again, he learns that "The books just seem to know to go where they'll be found". Well, that would certainly make a lot of library jobs easier.
There are several other scenes in the library, all seem to involve some sort of confusion, yet are strangely comforting to the Time Traveler. Again, this librarian could easily relate to the feeling.
As with most time travel stories, it is best not to over think this one. It would be too easy to drive yourself crazy with questions about logical fallacies, something else the narrator himself recognizes.