It is not that the ponds are built on higher ground, it is that they are built above ground with substantial embankments that would sit well above any conceivable flood level.
The photos that you have been seeing were taken near Calama. A river is a nice place to build a town in a desert - until it rains. Topography was not kind to them.
At 120km north of the Salar, Calama is a fair distance away in weather terms, but not far in news media terms. Given the economic significance of these lithium plants within the region, I would be surprised if the news media had missed something dramatic.
Some numbers - the Salar is approximately 3,000 km2. It sits in a basin of around 120 km long (N‐S) and 60–90 km wide (E‐W) - ie a catchment area of around 3 x the area of the salar which sits at the low point within the basin. See the map at this link
elevation map...They have had around 70mm of rain at Misnal Airport (the landing strip in the middle of the salar) since Jan 29. The heaviest 24 hours being around 17mm on the 30th. Some rain will have infiltrated the soil, some will have run off and accumulated in the salar (which is about one third of the are of the catchment so you can get some idea of the maximum potential flood height... Not enough rain to overtop the embankments.)
But what about raging torrents ripping up pipes etc?
There is no raging torrent of water rushing across the salar and sweeping all before it. It is an endorheic basin - water flows in and nothing flows out. It stops there until it evaporates or infiltrates. Flow in the middle of the salar - not very much...
A glance at Google Earth will show the location of a few sediment fans in the Salar that indicate where water has flowed from the hills in the past. If you dial back through the historical photos you will see that the fans are essentially unchanged since the earliest photo in 1984. The fans nearest SQM are a long long way from the plant. The fan nearest ALB is somewhat closer and directed away from the plant - it was already there when they built the plant.
The ALB and SQM news desks are both silent - given the headline stories, they are hardly likely to duck their disclosure obligations. It does rather look like business as usual (no doubt with some minor disruption).
The lithium operations were not destroyed in the great Atacama flood of 2001. Nor were they destroyed in the heavy rains of 2015 (which were possibly heavier than the recent rains.) I feel no reason to believe they have been destroyed in this recent weather.
At this stage, I would be looking for a very short term reduction in output and fully back to normal within a few weeks. I think your original estimate of a 2 year wipe out will be wide of the mark. The flamingos will remember the rain longer than the investors will.