I work at a college and we, too, have a central office that coordinates accommodations. The office collects all of the documentation and then sends it out every term to all of the course instructors for that student. The course instructors do not know the nature of the disability, but are instructed to provide specific accommodations. The students who need extra time typically take exams in the testing center instead of in the classroom. Most faculty are quite willing to provide accommodations, although I do know of a professor who refused to caption videos for a hearing-impaired student. The student had to switch to a different class because she was missing too much information from the videos.