A partially inflated balloon is placed inside a sealed container as air is pumped out of the by syringe. As the pressure of the container is reduced, the volume of the balloon increases. The pressure inside the balloon decreases.
Note that the pressure inside the balloon is not equal to the pressure of the container. The number of air molecules in the balloon is fixed. As the pressure of the container decreases, this creates a pressure difference inside and outside the balloon. This causes the balloon to expand and its volume to increase. The number of air molecules per unit volume inside the balloon decreases, hence pressure inside the balloon decreases.
But as the balloon is elastic, the wall of the balloon is stretched. Hence the pressure of the balloon will be greater than the pressure of the container. Refer to the video below.