Initially, the temperature of the air inside the bottle was normal, 20 degrees. When they put the matches inside the bottle internal temperature has increased. They put the egg, the fire has been extinguished and the air cooled. As a result, the temperature is reduced internal air pressure is reduced. The external atmospheric pressure is greater than the inside, the egg goes down.
OK for your explanation. See in red : some sentences are not clear to me. Check with your teacher Anton a way to express them correctly.
N.Hoang
2nd revision. OK