Could this be a 5V to 9V/12V USB to DC converter?
I recently visited an electronics shop in Asia where they sell this item (see below).
Could it really be that this product converts between 5V to 9V/12V? How would that even be possible? Wouldn't it be necessary to have a bigger adapter/transformer?
They can be constructed with no transformer at all, though other switch-mode supplies, such as the isolated Cuk converter and the flyback converter do make use of transformers. In those cases, because the switching frequency used is much higher than mains frequency (50 kHz through a few MHz are common frequencies) the transformer can be quite small --- perhaps on the order of 1-2 cm3.
Simple step up power supplies made out of switching regulators require no transformers. They work by charging an inductor or capacitor, then dumping the power as well as the input to the required voltage. They typically consist of a ic, a diode, an inductor and a few caps and passive components. See this picture of one without a case.