I believe the links that I saw claimed that you needed to pay for "60 days" of game time. This is probably why people have been using game cards so that they can get the mounts immediately. Someone correct me if I am wrong.

Edit: source

How can I earn the exclusive in-game mount?

For each person you refer who upgrades to a retail version of World of Warcraft and purchases two months of game time, you will be able to give a character on the account you sent the invitation from an exclusive in-game zhevra mount. This unique mount can be claimed through the website, is only available to Recruit-A-Friend participants, and can only be applied to a single character.