PWM is Pulse Width Modulation. The 4-pin connector is essential for PWM control and yes, a PWM controller cannot reliably control the speed of a non-PWM fan (3-pin).
Basically in the old days you controlled the speed of the fan by changing the voltage, so higher voltage = faster fan, slower speed meant you turned the voltage down.
One free way to reduce fan speed is to use the 5V and 12V rails to provide 7V to the fan - and if your fan can operate at that speed, use the 5V rail to power the fan instead of the 12V rail.
Anyway in PWM fans the controller powers the fan only part of the time and switches it off the rest of the time. The ratio of on to off times is known as the pulse width, with slower speeds attained by turning the fan off for longer. In actual operation it's not that simple as the fan needs to maintain speed between 'pulses', but this is enough to understand the principle.
That eBay controller will work just as well, though the output rating needs to match your fan's power draw. 10W is just around 0.75A so ideally you should not connect a fan with more than 0.4A rating (you have to factor in that unbranded stuff always runs below spec).