Logging in with your first character awards one achievement which gives you two transmog items. To get the remaining two you need to log in to another character of the opposite faction.
Once you've logged into both you will get the achievements on your account, and in Legion the transmogs will be crosscharacter, so it does not matter which characters you get them on.
The items you get are the following:
Replica Lion's Fang
Replica Lion's Heart
Replica Blood Guard's Cleaver
Replica Staff of Gul'dan