Hey Jasper,
the spindle coolant pump is usually switched on and off by the VFD, not the CNC Controller. VFDs have outputs specially for that, and only the VFD knows when and how fast the spindle runs, also the usual cooling stations are able to switch an alarm if the coolant temperature or the water flow are not in
the allowed range, and VFDs have inputs for receiving that and are able to stop the spindle then.
Also VFDs like the WJ200 offer the wiring of a smart Emergency Circuit (it’s in your VFD manual), which also can take care of halting the g-code program of the CNC controller in case of spindle error.
If you have a Hitachi WJ200, the manual contains information about both topics.