I believe the Nerevarine left before the crisis started. He wouldn't have known.
It's really hard to state anything, until the devs/canon authors tell us so, but one could speculate that since the world of the Elder Scrolls is, in large part, driven by prophecy (as contained in the titular Elder Scrolls), that certain prophecies may have come to the attention of the Nerevarine (or, as is often the case, the Nerevarine may have been ignorant of the prophecies, but propelled along by them, anyhow).
Since he went off to Akavir, it suggests that it wasn't his fated role to be the Champion of Cyrodill, and the fates had other adventures for him/her in Akavir. At this point, I don't think it's going to happen, but I had hoped that maybe Bethesda had been planning another game based on the Nerevarine's adventures in Akavir, which would have been contemporaneous (lore-wise) with the events in Tamriel.