Few fish will eat caulerpa. It's poisonous. Some purple tangs will, and thrive on it---but you have to test the individual fish.
Another way to fight it is to get a BIG refugium with lots of cheatomorpha macroalgae, that will sop up all the phosphate it feeds on. If you have room for a big sump there is now one sold that is 30g, with 20 of its gallonage available for a refugium, especially if you mount your skimmer external to the sump.
A third way is to run phosban, that will also sop up phosphate.
Phosphate comes in several ways, from the topoff water [non ro/di] and from fishfood. It's almost inevitable it accumulate if you don't have a way to remove it. The refugium is most efficient, and you can actually sell the excess algae to other reefers. Not to mention it breeds copepods like crazy, which helps keep down the film algae.
Of urchin species, tripneustes gracilis will eat caulerpa.
So will a scribbled rabbitfish, which is itself venomous, and which will shortly take after anything green in the tank: I had to get mine out before he ate my frogspawn.
