This is correct.
The motives of the murder are between the contractor, the Night Mother and Sithis. Your motive is to get paid.
Ehh... I'd argue about the "Sithis" part. Sithis (Padomay) is a force of nature. Entropy, decay, the inevitable degradation of things towards chaos, where Anu reassembles them back into new things, which persist for a time, but eventually degrade and once again fall apart into chaos.
There's no need to worship Sithis. Sithis will claim its due, one way or another, your participation in the process notwithstanding. As someone in the lore forum once pointed out, worshipping Sithis is like worshipping gravity.
However, It's widely believed that the Night Mother is a manifestation of Mephala, the web-spinner. Toying with mortals and convoluting intricate schemes of intrigue, suspicion and death is her sphere. In the end, it kinda makes sense.
Edit: Spoiler tags removed, since thread was moved to spoiler forum.