Velvet has two components: the backing (what you see on the inside), and the pile, the fuzzy part that sticks up. Either of those elements can be made from different fibers. For example, "silk velvet" is actually a silk backing with rayon pile, and very expensive. The silk gives it its beautiful drape, though the visible part is rayon.
Broadly speaking, viscose is a type of rayon. Probably these velvets have a nylon backing and viscose pile. The viscose is an imitation silk, while the nylon is very light but strong.
Shine can come from the material. Usually silk is not that shiny; synthetics are more likely to be shiny. It also can depend on how it's cut. Usually velvet should be cut with the pile pointing upward; it's counter-intuitive but it gives a richer look, darker. Also, a reflective material usually has longer visible threads. So the pile may actually be longer, which gives more length for reflection.
I am not sure at all if that helps you find the right thing, however. You may just have to go by appearance. There isn't a standard that I'm aware of for material in these cases. I prefer cotton velvet, but it tends to be more stable and not very drapy, so you're unlikely to find it in tops like these.