When you say "It works like a charm", does "charm" mean "magic"?
5p)Jekyll & Hyde is “forever.” No musical is as powerful and beautiful as this one. I have seen it many times, twice at Star Theater, and it will never be boring. Every time it is different, but still of the highest standard of quality. Outstanding work! It works like a charm.
I don't think so. That may have been the source of the original meaning, but the phrase has become an idiom. It simply means: it works perfectly every time.