Not sure you can get an accurate answer. Timelines are still a little off, League Lore isn't like Dragon Age where most lore is actually dated by year, Runeterra has more vague 'This happened'. The issue comes down to Vastayan's ages and the timeline. These species had to develop and change over a lot time right? Split into clans and species, move away from Ionia (see Nami) and many other things. I doubt that this happened within just a few generations but thousands of years.
Although only from the wikia page:
"Remains unexplained how the Great Void War happened, as it was prior to both the Watcher's arrival to Runeterra and the conception of the Voidborns they created."
Voidborns were apparently created in response to Lissandra imprisoning the Watchers.
Icathia Void stuff is really recent compared to Lissandra stuff as her stuff happened long before Shurima even existed. Most likely scenario is that the Great Void War was a Targonian response to Voidborns entering Runeterra's realm, it was the start of the demise of Targon as a mighty Empire and the 'humans' of that era fled to the opposite side of the area we know of, so Targon all the way to Ionia where they created the Vastaya.
But this is only speculation. sorry.