Stalactites ( think “T” for top) do drip down from the top as you describe. They will continue to to so as long as the ground water conditions above the cave remain unchanged. I have no information on this detail for this cave but conditions could have changed and dried up millions of years before the painting were done and remained that way. Those stalactites could have been massive “ canvases” for that Neanderthal painter and way older than the paintings themselves.
Stalagmite... G ground
That's the way us Neanderthals were taught to remember.