Circuit Breaker installation

It sounds like you may be mistaken as to how this is wired, or that perhaps I'm just not understanding your explanation. As others have mentioned, it's not possible to get 240 volts from a single pole in a 120/240V split phase system. Each tandem breaker provides 2 120 V circuits, this is true. However, if you measure between the terminals on a single tandem breaker, you'll get 0 volts. This is because the terminals are both powered from the same leg, and so are at the same voltage potential. If you measure from a terminal on the top tandem breaker to a terminal on the bottom one, then you'll measure 240 volts. This is because each breaker is connected to a different leg, which are each one half of a 240 volt circuit.

With all that said. For this setup to work, one appliance would have to be connected to both breaker. Something like this...

Notice that each appliance circuit has one wire connected to each of the tandem breakers. In this situation, you'd need a device like Speedy Petey shows.

Which ties the breaker handles together, to provide common trip characteristics.

Notice how the inner handles are tied together, and that the outer handles are also tied to each other. This way if either trip (or are turned off by the user), the entire circuit is shut off.

If this is wired the way you've explained, where the dryer is connected to the top tandem and the heater is connected to the bottom. Then there's some magic going on in those breakers.

Commonwealth countries normally use British standards in electrical wiring. For household wiring, there will be two distinct outlet from the distribution/circuit breaker board. One is 6A lines for the lighting circuits, and another one is 20A lines for all power outlet sockets. Lighting circuits are wired using 1.25 millimeter squared wires and the power outlet wires are 2.5 millimeter squared copper cross section area.

So, what you might have read from the internet is, anything connected or plugged in to the outlet socket is protected by the 20amp breakers. These breakers are rated actually to protect the wires in the house wiring, not to protect the appliances plugged to the sockets.

Properly rated fuse is already attached in your appliance power plug or embedded in its internal wiring. The 200Watts chiller is definitely consumes less than one ampere nominal current and its startup current may be three times higher, no way a 20Amps breaker will protect it unless it fully burnt and melt down.