Without getting an electrical engineer to open up the box and have a look we can only speculate. There are 2 or 3 likely reasons why this is working -
The box will work at 5 volts (or less), and has some voltage regulation circuitry to
carry out this function. This is quite common, and "voltage regulators on a chip" are
cheap and ubiquitous. It is possible that the 12 volts is only there, effectively to
act as a starting point and is then down-volted, and that the input voltage could
actually be quite a wide range.
The voltage regulation circuitry in the board itself may be "correcting" the voltage
upwards to the desired voltage. This kind of circuitry is not unheard of.
That said, I'd suggest against using a 5 volt supply for a 12 volt device. For a start, if it really requires 2 volts (or close to it), you will have a problem because 12 x 2 = 24 watts, while 5 x 2 = 10 watts, so the power supply is under-specced to do the job at maximum load. Although this could work, it could be damaging componentry.
Similarly, using a lower voltage supply (particularly 5 volts, 9 volts may have been OK), could be providing a lower then desired level of power to the chips. This could run, but might land up causing errors. I'm sure things have moved on since when I studied them, but a lot of chips were designed around 5 volts (but would work with less). If you are providing 5 volts input and the board has a common LM7805 regulator or similar, the actual components on the board will be getting less then the 5 volts required as this chip requires a higher input to produce the correct, stable output. While I don't know what chip is in the device, something like the LM7805 is extremely common to do voltage regulation (although typically at < 1 amp, but you get variants which handle more current)
I'd suggest getting a 12 volt power supply with 2 amps (or more) and using that. Even a (to be stupidly extreme) a 500 amp supply would not do any damage to the equipment as the equipment will only take the current it needs.
Shorts answer: the internal voltage regulator accepts a range of voltages. (example speculative: An LM7805 +5v regulator can produce +5VDC when supplied 3.6VDC to 40VDC (with provisions for anti hysterisis, and current supply)) – j0h – 2017-10-07T11:46:46.283
1I wonder if the person you bought it from mixed them up? It's not a massive voltage difference, so it's coping, but I would personally contact the seller and say "I paid for the adapter that came with the router, not one you had lying around!". Well, maybe I'd be more tactful than that... – Austin ''Danger'' Powers – 2013-06-30T05:12:38.910
1Why does someone down vote my question without any comment? If you happen to know the circuitry inside and can explain why it works, why don't you tell us? – LWZ – 2013-07-01T17:51:25.367
2When people down vote a question without leaving a comment it often just means they couldn't think of anything intelligent to say, or it took them out of their comfort zone in some way. Don't worry about it! – Austin ''Danger'' Powers – 2013-07-01T20:02:03.247