What does "out-titration" mean?
It does seem oddly phrased, but is still understandable. The paper explains how the combination of low zygotic transcription and increasing amount of DNA due to rapid cell division can function as a switch to trigger the mid-blastula transition. Before this event, most factors in the cell are of maternal origin (ie they are not being expressed in the zygote) and are thus in limited supply. As cell division progresses, the stoichiometric ratio between these factors and DNA decreases until, eventually, there is more DNA than these replication factors. At this point, you could say that the DNA has titrated the replication factors in that there is no unbound form left. This is analogous to the equivalence point of acid-base titrations commonly encountered in first-year chemistry courses.