If Joy was murdered at say 22.50, that would mean the killer would have to hang around for almost half an hour then make the call to the Police. If you had just killed someone you would have to be a very cool customer to do that.
Your natural instinct would be to get as far away from the scene of the crime as quickly as possible,imo,but it certainly can't be ruled out.
The killer seems to have spent quite a long time in the flat, before and after the murder.
Joy had two autopsies and both coroners said she died from multiple injuries. She had ligature marks around her neck, so the killer probably tried to strangle her.
The coroners don't seem to have confirmed if Joy was raped. A lot of the early newspaper reports say she was raped, but in later years the reports say she was sexually assaulted.
The autopsies confirmed (from the lack of smoke in her lungs) that Joy was already dead when the fires were started.