Why does an induction motor work as generator when running at a speed greater than synchronous speed?
When normally running from an AC supply, an induction motor runs at synchronous speed minus slip speed. The slip speed is determined by the amount of mechanical load attached. More load and the slip increases to allow the current induced in the rotor to rise and enable more power to be provided to the load.

If you were able to spin the motor and spin it at exactly synchronous speed the current taken by the stator would be zero (apart from the ever-present magnetization current). The voltage induced in the rotor would also be zero.

So we have the scenario that (ignoring magnetization currents), the stator current is zero at synch speed and rises (almost linearly) to some "full value" at maximum mechanical load.

Why should it be a surprise that spinning the motor at faster than synchronous speed (mentioning "sync-speed" absolutely implies it is connected to an AC supply of course) it becomes a generator?

Answering a bit more, the reactive "power" in the rotor does not contribute to output power when driven as a generator. Output power (into say a 3ph supply) is input mechanical power minus generator losses. The magetization currents in rotor and stator are just a means to an end.