They aren't reincarnations, as even Romulus became a god after death, they are Echo's, sometimes called shadows or doppelgangers. Twins born under the umbrella of Gemini, as they are now twins who shared their immortality and remain constant in the night sky. And because of Gabby and Ella's Greco-roman connection is why they only have access to those spirits, every set or magic or demi-god twins technically can be born under the Gemini even Helen of Troy can carry this Origin depending on how the character is imagined. Meaning that like the original brothers, their inherent magic allows them to share with each other, which is extended to all other echos or shadows. It's a complex origin, because it manifest multiple times even in the same generation, but due to the inherent abilities that come when channelling it, means all that hold it share a connection. Sorry if I made it too pointlessly complex. 

This quote from Wikipedia, kinda holds the basis of the Gemini origin. 
"Twins appear in the mythologies of many cultures around the world. In some they are seen as ominous and in others they are seen as auspicious. Twins in mythology are often cast as two halves of the same whole, sharing a bond deeper than that of ordinary siblings, or otherwise shown as fierce rivals. Twins can represents some "other" aspect of the Self, a doppelgänger or a shadow. Often the twin is the "evil twin"[citation needed], or one may be human and one semi-divine. The twin may be a brother, or a soul-mate, such as the "civilized" Gilgamesh and the "wild" Enkidu... ...Twins can also be shown as having special powers and deep bonds. In Greek mythology, Castor and Pollux share a bond so strong that when Castor dies, Pollux gives up half of his immortality to be with his brother. "

And Venetus in the game resents Ruber, I know my Mythology it was a large part of my degree.