Sidney Poindexter's world is part of the Ghost Zone and he lives in a mirror dimension which is not actually the past, but a ghostly recreation of what high school was like in the 1950s for him when he was alive.
The ghosts of high school students from 1950s, it's unknown if they're the souls of dead students. They might be possibly appear to be ghostly copies or manifestations created by Poindexter's mind and environment.
Poindexter is the actual spirit of a former Casper High student who was bullied during his life, he's not the ghost copy. After his death in the 1950s, his ghost ended up haunting a mirror dimension, a twisted reflection of the school.