Making a noise with the hot chocolate tub

 The empty tub of hot chocolate flakes has a membrane at the end labelled A.

When I push in the bottom of the container (red arrow below) the membrane makes a noise when I push it in fast but not when I push it in slowly.

There is a volume of air trapped inside the container. It is able to get out through the tiny gap between the two parts of the container, as shown by the blue arrows. There is clearly a maximum flow rate through this gap. Pushing in fast means that the squeeze of the air into the top of the case happens faster than the air can leak out of the gap. This increases the pressure enough to pop the membrane out, making a noise. It then flexes back, so you get a double sound. It only happens by being pushed outwards. Pulling the bottom half out again fast makes no sound.