And the thing is, Namus states:
1. Yellow colored ring with a pink-red stone setting and four small clear stone settings on the sides of the ring.
2. Yellow metallic ring with a small red stone setting
And before I even saw this Namus link, the photos of Amethyst Doe's rings, do not look like an amethyst stone to me.
They look pink-red to me, which could indicate a garnet (which can come in different shades), a tourmaline (which can come in different shades), and also a ruby(which can come in different shades). It could be a spinel also. If it were a garnet, it could be a rhodolite garnet.
So if it was a synthetic ruby or real ruby, it could be for the birthstone of the month of July.
Garnet is a birthstone for the month of January.