My understanding of it is thus:
-You queue on a toon of Class/Spec
-It puts you in relevant challenge from list below
-Upon completion of that challenge, you unlock mog set for that class
-So you will need to complete it once for each class
So 12 times you will need to complete for all items.
This is just a list of 7 potential places you will need to go. So if you have a mage and know Impossible foe like the back of your hand, roll in as fire, but no mettter if you do AIF as fire, TGQF as arc or TTT as frost, completing any will earn you the mage TMog set
TLDR
The only thing the seven completions is relevant to is needing to complete all seven to get the mount, all xmogs are class specific