I can't find this answer on google or here so I decided to make an account and ask you guys. Here it is:

How do members of the order inhabit the same plane or dimension of Silent Hill as the protagonist? Since they are in the cult do they have special rituals that allow them to change dimensions at will? If the protagonist say Heather is in the nightmare world does that mean the cultists in her proximity will share her world? Do the cultists live in a perpetual foggy world or do they also visit the real world?

I know Twin Perfect says there are no parallel dimensions which would explain this question, but I don't believe them.

They don't have any special priviledges to enter the Otherworld, and most of them don't know it exists. In the first game Alessa grabbed a bunch of victims into her world to punish them (same with the movies), and in the third game they get pulled in because they're already part of it or have reasons to be there like in the first game. There's the possibility Claudia uses her perception powers to make Heather perceive, and thus bring in, ordinary cultists for her plans, but that's about it.

Thanks for the response that makes sense now. I know the town has always been a place of power but when did people start experiencing the other world and the fog world? Was it the power of Alessa that tapped into Silent Hill or was it always such?

There was always a spiritual power that allowed for meeting the dead and spooky phenomena, but the Otherworld and Fog World are creations of Alessa, which sort of intercept the original power, like placing a dimension inbetween the real world and the spirit world.