It depends on which ATC system is being used. Pretty much all systems though will make an aural alert of some kind, and usually the label will change coulour to red and will flash with an indication of what kind of emergency is being experienced eg. HIJ, RAD, EMG. It will usually show on all positions so even if the controller concerned has recently undergone a frontal lobotomy and happens to miss it, everyone else in the ops room will see it.
Hope that helps.