I don't know much about these. I bought one years ago, and have only just got it up and running. Mine is variable temperature and it can be switched from ice to cold water.
For my purposes (primarily fermentation temperature control) I see little point in using the ice position, as I foresee more chance of undershooting the set temperature.
On my machine there is the compressor side, which is controlled by the thermostat and the ice/cold water switch, and the pump side which I think turns on and off when the compressor turns on and off. However, the pump is connected to its supply by a plug (euro plug?). I intend to unplug this and simply control the flow of coolant, by controlling the pump with an Inkbird, with the thermocouple in the fermenter, and simply allow the water bath to constantly stay at the set temperature. In this way it will be providing effective chilling straight away.
Can you do the same thing by allowing the chiller to arrive at it's fixed temperature, and then controlling the action of the pump?