Update your pet collection and watch the magic happen.
Whenever you visit a pet's profile, it will load up the data associated with the pet in your own collection. So if you have a rare level 13 version of the pet collected, its stats calculator will default to those values and breeds, allowing you to adjust the stats of your own pets
Pretty neat, right?
The reason you're seeing only poor quality pets is because your collection hasn't been updated yet. So as I said above, update your collection and all will be as it should be.