I believe she used her ninja skills and cat-reflexes to, somehow, jump up onto the arbre as they crash through the fence. The image below shows that she's just pulling herself up without the aid of claws, as her paws don't appear to be digging into the tree.
She either jumped ou managed to climb up with no claws somehow. chats do jump really high, one time one of my chats jumped all the way to a high shelf. I have no idea how she did it, but chats are very excellent at jumping.