It's a safe bet this is normal aggression for the species. This one is known to be a bit nippy which is why in the profile it suggests never to combine them with slow sedate fish like angels which are a temptation. But within the group, this is natural though it can usually be curtailed.
Characins need a group, the more the better, for various physiological and social reasons. Sometimes being in too small a space (to the fish) will aggravate any natural aggressive behaviour; so will being kept in too small a group (less than 5-6 has been scientifically proven to cause this, even in otherwise peaceful species). So a group of 6 or even more for this species, and in sufficient and suitable (to the fish) space usually helps.
When a group of a species is placed in a tank, they eventually settle in and the tank becomes their "space" or territory. All fish, and I mean all, are territorial to some degree. Many do not exhibit any issues in this regard, while others (cichlids, gourami) are very obvious in defending territory. All characins are territorial. When more of the species is added, sometimes this is tolerated, sometimes not, depending upon species and also on other environmental factors. Which is why I also recommend acquiring a large group of any shoaling fish together. Often with tetra this is irrelevant, but sometimes not. That may be part of this issue. Or it may be the natural frustration of the original 3 finally coming out. When ever an aquarist in such situations says their fish are doing fine, my response is, just wait, it may not last. No one knows why some fish are quieter than others in the same species; all we do know is the inherent traits, and that these can be triggered by several factors.
This is a species that would be better in a longer tank. This would work to alleviate the space issue they now face. Length plus lots of plants, wood, or similar to break up the space always helps with shoaling fish that like to swim, as this species does. You can read more in our profile, click on the shaded name Black Widow Tetra
Hope this helps explain things.