Fish eating anemone

There is one thing I don't quite understand about fish eating anemonies (pictured) - supposedly the thing in the middle is the business end of the the whole 'fish eating' part. Since these things don't look like it's the speed that works to their advantage nor do they exactly try to hide themselves for some stealthy action, I'm unsure as to how they bring food to the table.

I've spent good amounts of time on several dives observing these creatures, but I'm yet to see one successfully catch some lunch. In fact, it seems like the little fish avoid these things like the plague. Anyhow, they do make pretty satisfying targets for photos, with what all those tentacles and the crazy colors and patterns in the middle.