There are 5 workers per level. Simply put out the fire near them. Press X near a worker to get them to follow you. Take them out of the room on fire and back to the initial starting room. This will unlock the trophy.
When you enter a room that contains a worker, they will cough if there is fire in the room, and whistle if there is no fire. Listen out for this as it is easy to not spot them sometimes if they are hidden in a corner and such. Just note there might be more than one worker, so double check before rescuing one and returning to find a dead worker on the other side of the room.
The workers and cats do not get a health bar until you enter the room. So if you stand at the door then you can put some of the fire out that is near them first. This makes it easier.