The outer reason is that it was gifted to them by a devotee who was probably inspired by the image of Shiva wearing a tiger skin and some Yogis using the tiger skin to sit and meditate or the animal itself as a vehicle. Of course Sri Aurobindo never used it but as a symbol of his yogic stature it was gifted to him.
Incidentally the Puma or mountain lion, a close kin of leopard and tiger was Sri Aurobindo’s favourite animal if we may say so.
Finally there could be a possibility of some kind of occult working on the feline species which the Mother did speak of.
Of course they have not spoken anything about it directly.
Affectionately,
Alok Da