THere were probably several times when the sea level increased permanently by feet or meters. If indeed a boloid event caused major disruption and tsunamis 13,000 years ago, this would have become part of oral history for many generations. Although the Agassiz even would only have raised the worlds oceans by a foot and one half; first, since the water flooded into the North Atlantic and the Caribbean very suddenly, it may have caused tsunami type conditions striking Europe and North Africa. The initial increase in water level would have been on the order of one or two meters before the levels settled down world-wide, not to mention possible much higher tidal surges (tsunamis).
With an oral history of other significant rises, coastal and marshland peoples might have considered it prudent to move the settlements inland permanently.
I think the Incas probably took to the mountains because of tsunamis.