It's not a terribly invasive caulerpa, so not a huge worry. However, with it growing on your rocks it will be difficult to remove completely, should you decide to. I had some growing on sand and it was easily removed.
I'm definitely no sea star expert, but it looks kinda like a chocolate chip sea star.
I had a similar situation with an anemone. It disappeared, presumed dead. Months later I found it, and it was much smaller. Not an apples-to-apples comparison, but similar. A better comparison would be a shrinking sea cucumber. In many aquariums, there just isn't enough food to support even one cucumber. So they gradually shrink down to nothing and disappear. I suspect this happened with your choc-chip star. It starved, shrank and disappeared. Now your tank has matured and maybe produces more star-food.
From Wikipedia: Horned sea stars seem to be opportunistic carnivores; adults are known to prey on most sessile life forms including hard corals and sponges in aquarium. In this same setting, they will hunt down snails and eat them.