This happend yesterday for a friend of mine.
They where going for the heroic Obsadian achivement realm first.
Right before they encounterd the boss it sayed that the realm first was for another guild. But they didnt killed it.
This is what happend:
The guild that did get the achivement had a person that just transfered to our realm. On his old realm he had killed the dragon on heroic. So he had earned the achivement there.
So when he entered the instance it gave the guild the achivement right away because on our realm it was not killed yet.
A few minutes later my friend killed with his guild the dragon realm first but, ye, they didnt get the achivement.
So short story:
If you would have a realm first achivement and you transfere to another realm and enter an instance with a few people where its not been killed yet, all that people getting the achivement right away if you enter it.
I'm sorry for not having screens. It kinda hard to prove this with screens, we where also kinda stunned that this happend so forgot to make any.