Copper probably does only work on the free swimming stage, but I believe it also kills parasites on the fish. Typically fish are treated with copper for a few weeks, ensuring that all the parasites go through the swimming stage and are killed. But, I've read that copper is also pretty toxic to marine fish; especially tangs, where it attacks microbes that they need for digestion. And it kills bacteria necessary for biofiltration. So, it's a pretty drastic step, but it definitely will kill the parasites. It works best if you have a big quarantine system that has copper running continuosly, like they have at some high quality fish stores. In those systems, apparently the biofiltration can adjust to the presence of copper somewhat, and the size of the system helps to keep waste products like ammonia from building up. But, if you're going to take a couple of sizable fish out of your reef and put them in a bare 10 gallon, then treat with copper, you can expect a quick ammonia spike, which means lots of water changes and constant adding/testing for copper levels. Ideally, then you would continue quarantining the fish without copper, maybe with some ozone or UV sterilization, to allow them full recovery from the stress of being subjected to high levels of copper. My guess is that this is what the best fish retailers do with all their incoming wild-caught stock.

The moral of the story is, suport fish stores that sell healthy fish, and then take the steps needed to keep your fish healthy enough to resist the effects of parasites.