The version of Sithis the DB seems to worship is more of Shor than anything. However, a bunch of psychopathic sociopaths are not going to have the best grip on reality.
But, Shor has been known as the soul of Sithis, who is the soul of Padomay, making Shor the soul of the soul of Padomay. So, it's close enough.
As to why they believe killing gives him jollies, well, think of Shor as mortality, and they worship the side of mortality that involves death. As for whether they care or not, I say no. For Sithis, it's like sacrificing to gravity. In the end, you'll still fall down at 9.81 m/s^2 just like anyone else.