The way I understood it, the actual engine fan doesen't change speeds. It's always spinning at a medium rate. That's why there's a mechanical clutch which doesn't allow it to spin up to the engine's revs (too tight), but also doesn't let it stop spinning (too loose).
There is ANOTHER electrical engine fan (auxiliary fan). This one has 3 speeds: off, low, and high. If you have a mechanical clutch fan (above), you should really only hear this come on at idle when there's little airflow into the rad. It is controlled by a temperature switch that goes into the radiator. Perhaps if this is the aftermarket one you're talking about, it's no longer connected to this switch, or doesn't correctly interpret the readings.
BTW you don't want a fan to be too fast or on when it's not supposed to be, since you may run the engine too cold.
1998 BMW 328is - summer
1994 BMW 325i - daily
1992 BMW 325i - gone
1988 Mercedes Benz 190E 2.3-8V - sold