Is exotic animal defined as non-native animal? That's too broad a definition.
If that's implemented strictly, I would say a lot of cats and dogs would be banned because most breeds of cats and dogs are not native. Let's say you are in the UK. So, as far as the UK is concerned, Shih Tzu dogs and Persian cats are not native animals. Or if you are in the US. Then, as far as the US is concerned, Akita dogs and Sphynx cats are not native animals.