The term Tandem can cause some confusion. There was a tandem breaker that used 1 pole from the bus and had 2 15 amp ccts available. This breaker would not be appropriate for a shared neutral unless the neutral was good for 30 amps and even then would still not be code compliant. there are also side by side mini breakers that also used a single pole off the buss. Again this would not allow a common neutral.
To share a neutral whether for 2 circuits from a 3 wire or a split receptacle both current carrying poles must come from a different phase so the voltage between poles is 240 volts and not 0 volts, In both cases there would be 120 volts to ground or neutral.
In the case of a split plug a 2 pole common trip breaker or tie bar is required.
A 3 wire circuit supplying 2 different loads and not on a receptacle with a common yolk can use 2 1 pole breakers on adjacent phases without requiring a tie bar.
