My 6 bloodfin tetras often chase and nip one another. I recently got 10 neons and they do the same. A friend has bleeding heart tetras and they do the same. So, I wonder if all tetras are fin nippers to some extent.
Meh, I kinda hate most tetras, they either nip or are incredibly boring. I had 9 glowlights that were fine for a while in my community tank(where there has NEVER been a single issue) and in time my beautiful lyretail mollies started showing nipped fins, then a couple platy, then my friggin sterbai cories' top fins. I saw them nibbling away at them when they were resting. I promptly re-homed them in my brother's african cichlid tank. Still mad about the little bas***'s, everyone else is finally just about healed up.
Not sure if rummys nip though, every time I see them in tanks they kinda just school together tightly and act more like danios, kinda indifferent to everything else. All the others are always nipping other fish or themselves. One of the petsmart tanks had (I think)black skirts and silver dollars that all the SD's had their tails completely missing, it was kinda gross.
I've kept glowlights before without any nipping issues, I've seen neons do some mild nipping. It depends on the species some, I've noticed deep-bodied tetras tend to be nippier.
Mine were full grown, you could watch them at night just literally munch on sleeping fish. They were very comfortable in the tank by that point, and would often spread out(they hardly schooled at all anymore) and creep up and do it.
I can't ever see owning any tetras again(maybe rummynose), they never do anything for me even in huge feature tanks at fish stores. To me they're a waste of bio-load.
I had to exile my blackskirt tetras to another tank. They were horrid nippers. Or maybe good nippers They really were relentless, so they joined my exiled skunk loaches.