My description explicitly hypothesised a universe that is entirely immutable, and where the passage of time is purely "read only". Your presence at any given point in time then would never mutate anything ever, any more than watching a movie mutates the movie.

EDIT: You can certainly imagine more "relaxed" models that would also work, where mutability is possible, but where constraints increasingly restrain which mutations are possible when looping back on itself, but an immutable model is the simplest to describe in order to illustrate that models that allows loops can be made self-consistent.