I would refer to this wikipedia article:
http://en.wikipedia.org/wiki/Ultraviolet
The section on "black light" explains that long wavelength bulbs use a phosphor to get the required wavelength of emission, and do not need quartz bulbs; nor do they need Wood's glass unless it is desired to eliminate most visible light - so this may be what was used in the display - fluorescent tubes with Wood's glass bulbs plus extra Wood's glass filters to completely eliminate visible violet.
The small long and short wavelength lamps sold to the public that I have seen in the past definitely have some visible violet that would be visible even through the glass case. Other displays I have seen also have visible violet light showing through the glass case. That is why I suspect this display has better filtering, perhaps not in the case glass but in the bulb glass or in an extra thickness of Wood's glass added between the bulbs and the samples. I did not notice how the light sources were arranged.
By the way, I have a cataract removal and lens implant in one eye. I requested and got a UV filtering implant. Even so, I can see deeper into the violet with that eye than with the 67-year-old brown-tinted natural lens in the other eye. I saw no UV effects in either eye. Some objects are noticeably different colors in the two eyes in daylight, and even in daylight through glass. A colleague who has one UV filtering implant and one clear implant sees even stronger differences.
In WWII, it was attempted to put fluorescent paint on carrier-based planes and illuminate them with near UV so the landing officer could see them clearly at night. This had to be abandoned, as it blinded the pilots when the vitreous humour of their eyeballs fluoresced, especially the young blue-eyed pilots who had less uv absorption in their lenses.