Does it happen on a certain day? I don't remember talking to Gardenia right in Front of the Old Chateau. The reason is because Rotom is the only one to find in my Sinnoh Pokedex.
After defeating Gardenia's in the Eterna City Gym you can then find her in Eterna Forest. Talk to her and then cut the tree behind her. Go up to the Old Chateau and on the second floor there will be a room with a TV. If you go there between 8 PM and 4 AM you can interact with the TV and Rotom will appear!