I think by virtue of the Prophets following a "non-linear time" (something which we as humans are 100% incapable of understanding) we cannot conclusively say that it doesn't make sense.
All we can do is take it at face value that they do not understand our concept of time, and that it took meeting Sisko for them to understand time. But we're also watching and learning about the Prophets from our point of view (the chronology of DS9), and not from their perception. It is entirely possible that meeting the Sisko was the catalyst for everything we saw in DS9, including Sisko being born and eventually being named Commander of DS9.
Its odd for us to think about a catalyst taking place linearly after the effect, but that's indeed what happens.