I've found out how it works just after contacting customer service for a replacement.
Until today, it rang once every four/five tries, sounding as though the metal was in contact with something and therefore being muted. It has failed me a few times when I needed it etc... I was growing irritated at this neat looking but useless piece of equipment.
After reading that dissatisfying sound production could be the result of having tightened the screw to tight, I took it off my handlebar today and tried it just holding it with my fingers. Rang perfectly every time. Not the loudest, but nice and clear, as it should! I tried putting it back onto my handlebar but the problem persisted, even with the screw lose to the point that I had to reposition the bell everytime I sounded it. And by the way, then just like before I contacted customer service, of course the metal was not touching anything, there being a good half centimeter between the bell and the handle on one side, and the breaks lever on the other.
Anyway, I tried it at different places and in different positions on my handlebar. Without there being any obstacle, for some reason (acoustics, I assume), it works very nicely at certain spots, and not at all at other spots, regardless of how tight the screw is. I've found a place where it works very well, tightened the screw as tight as it was before I thought that might be the root of my problems, and now I have a bell that works.
I guess the only drawback compared to other bells now (apart from the sound level that I understand is not as much as some people like and can find in other bells), is that you're not entirely free as to where to put it : it wouldn't work where I wanted it initially (close to my left thumb), and I had to find a compromise, the place where it works best on my handlebar. That's something I can live with, though, and I'm finally happy with my purcahse!