Your link points to the description of a device marketed as a "transformer", but obviously containing much more. It seems like this device is designed specifically for the use with 12 V halogen lamps.
If it was a true transformer (and nothing more), it would work at mains frequency (50 or 60 Hz), and you would have this frequency at the input (primary) and at the output (secondary). In this case, a cheapo multimeter would likely give you an acceptable reading when you were measuring the output voltage.
Your "transformer" seems to be a switching device. I assume it works like this: The AC input voltage is rectified to DC and fed to an internal electronic switch (likely MOSFET). This electronic switch chops the input current to an AC current with a frequency of 40 kHz (cf. your link, see output frequency specification!). This AC current at 40 kHz is fed into a transformer, and the secondary side of this transformer seems to directly accessible at the output wires.
I assume your multimeter uses a low-pass filter when it measures AC voltages, and this filter blocks most of the voltage at 40 kHz, giving you a reading of only 1.2 V when you should actually see > 11 V.
To be really sure, you could measure the output voltage with an oscilloscope. I am fairly sure you would see a somewhat rectangular waveform at 40 kHz = 40000 Hz, and not a somewhat sinusoidal waveform at 50 or 60 Hz like you would with an ordinary transformer.
For a voltage with a frequency and waveform like this, I would even carefully check the manual of a good RMS multimeter because even one of those might have a low pass filter around 1 kHz.
Note that in case (a) the ratio of the currents is negative while in (b) it is positive but the secondary current arrows are reversed. They both, effectively, say the same thing.
I've never seen it expressed as in (a) but I can see that it may make some sense to present an ideal transformer with current in from both sides as neither side is then assumed to be "input" or "output" but both can be inputs, etc.
(b) is the normal way of thinking in most electronics applications. You may find that (a) has its uses in electrical utility grid transformers where power can flow either direction to suit generation / demand requirements.
(c) and (d) should be fairly obvious inversions of (a) and (b) respectively.
It's not a problem, it's a convention. The dots show the phase relationship of the voltages. The AC swings positive and negative so coils could be in phase or out of phase. The dot ends are all in phase.