I had a 5-day embryo put in and they did the pregnancy test ten days after that procedure, and as I recall they said implantation generally happens in the first 2-3 days after the procedure. It obviously must have happened well before the 15-day mark because hormone levels are already changed enough to test.
I had several bouts of bleeding during my first trimester. They can't have all been implantation bleeding, and in fact the first time was a couple of weeks after pregnancy was confirmed. Each drop of blood that came out scared the living daylights out of me.