If a third landmark counter is put on Treasure Map by something other than the resolution of its first ability (as modified by any applicable replacement effects), you won't remove those counters, transform Treasure Map, or get Treasures yet. You'll have to wait until you activate its first ability again.

If Treasure Map leaves the battlefield before its ability resolves, you can't put a landmark counter on it. However, if it somehow already had three landmark counters on it before it left the battlefield, you'll get three Treasures.