My thoughts are that the outlet pipe from the hot water heater goes under the floor in the ceiling space where your island is. chances are it isn't insulated against radiating heat from the pipe. the tile is acting as an absorber and radiator. as the water flows through the pipe the pipe is radiating heat which the tile is absorbing and distributing, this is why the area is getting larger. try putting some kraft faced insulation between the floor and the pipe, or a piece of neoprene pipe insulation around the pipe.