After Yi Rong left to go back to his study in the imperial doctor's courtyard, the black-clothed man remain following Liu Yeyin. They didn't leave the Imperial Noble Concubine's palace. Instead, they made their way toward the palace's underground hidden room.
This kind of hidden room is not deemed unusual in a palace. Almost, if not all palaces have at least one of them. Mostly, these rooms are used by the occupant as a treasury so it is only natural that it is revealed only to the occupant and their trusted aid and the emperor. These rooms are windowless and have never seen the light of the sun. This causes the air in the room to be stale and uncomfortable to live in.
These rooms are noticeably sizable. Usually at least half the size of the palace's floor area. Lin Xulian also used the hidden room in the phoenix palace as a treasury and storage room for her medicines and dried herbs.