The key to this riddle is realizing that you do not have to pull the emergency switch in the first room, the entrance, and so that room will not lock down. You can leave it, and then return to it and go out the other door. And indeed this is exactly what you need to do so you can hit all 16 rooms and end in the exit room.
Once you know to leave and reenter the first room, there are eight possible solutions to travel through all the rooms and end at the exit. Because the first room is clear, you can backtrack through it to get back on the right track and pull the emergency switch in every room, saving the world from agonizing death by ancient virus.
Well since you know you are not one of the cursed you can go down a tunnel yourself but you want a good answer from the rest so you split the groups in three leaving two left. Let those two go down one tunnel and the other six go down two separate tunnels as well. When you all meet back 20 minutes later either you have found the tunnel or someone else. Now look at the rule majority rules. If the group of three has 2 people saying it wasn't down that tunnel then you should know it wasn't down that tunnel and one of the liars have been spotted. Same with the other group of three as well as the group of two. Judging by the answers the groups gave you, you should go down the right tunnel and head to safety while the spirits possessing the two people should leave and all is well.