of course the rules follow you. In the sense that you get 1 30 day extension from a visa exempt entry. The requirements might be slightly different from province to province. What you said initially was that if on a visa exempt entry you have to use laksi square in Bangkok. That is only true if you are actually in Bangkok.
which office what? If you mean Bangkok, it's laksi square for visa exempt extension. If another province, then usually just the local immigration office.
Bangkok has a separate office for visa exempt. I don't know of any other provinces that does. Just go to the immigration office. There are 77 provinces in Thailand, and more than 80 immigration offices.
it doesn't "follow you". As a tourist you get the extension at the immigration office that serves the area you are in (where your latest tm30 is done).