its your internet connection(or possibly really slow hardware), the server already got the command for the other person to use their mystery and waited for you to give a command in time, when you fail to give the command then the other person uses their mystery, then your computer gets the updated data and you see the mystery activate seconds after the other player triggered it.

from the other persons perspective he was probably waiting on you after activating his myst and was getting frustrated at how bad your connection was.