Does using Mnemonic Deluge on Skull Storm count as casting and therefore get me more triggers of Skull Storm?

So as I understand it, [[Skull Storm]] ’s self copying ability triggers if I cast it, so targeting it with something like [[Reverberate]] will only get me one additional copy. But [[Mnemonic Deluge]] reads that I cast the three copies, so therefore I should get its self copying trigger on each of the three copies, right?