I completed The Chaperone and Ace of Spades exotic quests and the Secret Achievement "An Exotic Journey" did not unlock for me.
Sometimes the achievements dont immediately unlock on xbox. There is a method to force them to unlock. In game open your character screen and click over to the settings tab. Hover over the 'log out' option and choose 'switch profile'. It will take you back to the title screen and then ask you to pick your profile. Do that and then when you get to the character select screen just pick your character and the achievement will unlock a few seconds later.