Something is wrong with the wiring to the ceiling fan or with the connections to the switch.
Possibly in between the last succesful test and the first unsuccessful use of that switch something has damaged the wiring (e.g. a nail into the wall? strain on the wires?)
I would isolate the circuit at the breaker box, test for voltage at the switch and then test the wires attached to the fan switch for unexpected continuity between live & neutral, live & earth. I'd then detach the switch from all wiring and test for continuity across it's contacts with the switch in each state.
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.
![common trip device](https://i.stack.imgur.com/p304Y.jpg)
Which ties the breaker handles together, to provide common trip characteristics.
![enter image description here](https://i.stack.imgur.com/A9CJW.png)
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.
Best Answer
AFAIK, Canada uses the same split-phase arrangement as the USA to deliver 230 V to the premises, with the center tap grounded as the "neutral" wire.
So yes, you definitely need a double-pole breaker. Both "hot" wires need to be protected from over current.