They aren't literally 'man-made' - like The Wolf said, it only means they've been selectively bred over many generations to have longer and longer fins. Kind of like the various breeds of dogs, cats, livestock etc. Though it may mean they are a little in-bred, it isn't realy a bad thing strictly speaking though it may well men they have slightly weaker immune systems compared to the wild-type fish. Anyway, the reason I posted was realy to say that the other long-finned tetras you saw don't necessarily have to be selectively bred. Black phantom tetras, angelfish, pearl gouramies etc are all fish with long fins - they occur like this naturaly in the wild.
When it comes to truly 'man-made' fish, I guess we'd be talking about unatural hybrids like flowerhorns, jellybeans parrots and blood parrots etc. That's a completely different topic altogether...
And then there's dyed fish which I would say is deffinately wrong - not even debateable.