...and I am playing the character who earnt it later, which date does it show on him? The date I earnt it first (on a different character to this one) or specifically on this characters date?
On all characters who have not earned the achievement you will see it in blue with the date the overall account earned it, but on alts that have also earned the achievement at a later date it will show in the traditional way (the way it currently shows on live) for that character with the date they earned it.