Hello OC!
EDIT: You can ignore step 1-6. You only have to log in twice on the character you wish to complete it with. Once to pop the Emissary and a second time to complete it.
After some searching on the forum today I did not see anyone mention this, so here I go.
The following method is only confirmed (by me) on EU servers.
A quick how-to for those who are doing the Kirin Tor emissary that popped today on EU. If you complete one of their WQs to meet the 1/1 requirement for the emissary you can get the completion on all alts that are eligible for WQs, without having to do the WQ on said alts.
This is the method I used to transfer the completion:
1. Complete 1 Kirin Tor WQ on your main. (I chose the one next to Shal'aran in Suramar.
2. HS to dalaran.
3. Log out.
4. Log into an alt character who you wish to complete the WQ on.
5. Move the alt to dalaran. (If you are in dala already, ignroe this step.)
6. Log out.
7. Log out and log back in again on the same character.
8. Profit, the requirement should now be met for the Kirin Tor emissary and you can receive your rewards.
Enjoy the bug and if you find any further information on this, please comment and I will edit it in.