From an engineering and physics perspective, removing most of the heat content from the wort with the tap water chilling system followed by a separate chilling event using ice or other super-cooled method is most efficient. Pre-chilling your water and using it to cool the very hot wort justs wastes the extra 'coldness'. The thing that matters is the temperature differential between the hot wort and the cooling water. Once most of the heat is removed and the wort temperature has dropped to the luke-warm level, then its time to employ the ice-chilled water.