When taming a new Hunter pet or moving them out of the Stable Master, the flyout does not update to match the newly added pets. For them to appear, you need to either use /reload or go to a new continent/instance. This is pretty inconvenient, especially if you're hoping to use your new pets asap.

Addon Version
10.2.0-retail

World of Warcraft Version
10.2

This should be resolved in the latest version.