I take it you are using three people to press the buttons up top. What you might be missing is that in 16-man, there is a debuff applied to the last person to press a button that prevents him from making the next action. This means that the person who pressed the fire button got the debuff and someone else was required to make the first move on the next puzzle.
It's up to you on how you want to solve that added feature.
thank you. I was not aware of this.
It would also explain why we got stuck when someone moved a piece that they shouldn't have.
Thanks! all is clear and we shouldn't have a problem now.