Technically this is incorrect, although the thrust of what you saying is right. If flying SQ or any airline from Changi terminals 1.2 or 3 you clear border control/immigration when moving from check-in to the main departures area where the lounges are. However you will not clear security, as this is done immediately before entering the gate for departure, and security closes strictly 10 mins before departure of the flight.

Note: once airside (ie once you have passed through border control/immigration) you cannot go landside again as it is illegal and can result in a substantial penalty.