The switch needs to be at the top of the radiator because that's where the hot coolant is immediately after leaving the engine, if you installed it in the outlet of the radiator you will be measuring coolant AFTER it's been cooled, meaning that by the time the fan cuts-in the engine temperature will already be too high.
That may not matter so much with an adjustable controller because you can "tune" it to suit, depending on the controller of course, some may not be able to be adjusted that low.
But a far better idea is to install the switch just under the thermostat (on the engine side), that way if the thermostat sticks shut for some reason at least you will know about it, if you're measuring temperature at the radiator (after the thermostat) but the thermostat never opens, your reading will never alert you until it's too late.
The problem with your fan(s) cycling too much is due to the hysteresis built-in to the thermal switch, some controllers allow you to set both "on" & "off" temps, some don't allow you to adjust the hysteresis at all, much like thermal switches.
It's been my experience that temp gauges actually go up (or "spike") when the coolant level drops below the sender as the air / steam is actually hotter than the coolant itself.