My initial viewpoint that we're against the Cult, along with the 3rd Party, comes from this, in the OP post:
One side or the other must win within a time limit proportional to the number of players, or everyone is doomed!
Also the quote you bring up doesn't disprove what I've said. It infers that you win the game when everyone that shares your alignment, no matter what that might be (Town or Cult), has that alignment until the end of the game. It doesn't mean that Town and Cult are allies in this. It was just laying down the end goal objective from a second-person viewpoint. Though admittedly it's kinda confusing and just my personal interpretation of it.