If you do the "For the Horde" or "For the Alliance" your new bear gets mailed to you. If you do the 100 mount achievement your birdie gets mailed to you.
On the basis of the "Have horde and alliance T9 bonus" this should work.
1: Be awarded and achievement mount in your mailbox.
2: Faction change
3: Accept the mail from the opposite faction
If anyone doesn't have For the Horde/Alliance, and is gonna do a faction change, can you confirm this?