They first appear in Danger Wears A Cape where they are seen throwing different items at the penguins until Alice tells them to cause pain somewhere else. Their backpack contained several comic books. In Operation: Neighbor Swap, Julien believes them to be giving him tributes of snacks and drink and climbs all over them, scaring them off. They appear again in Pets Peeved as the main antagonists of that episode as they seem to torture The penguins and The lemurs. They also seem to be part of a rich family and have personal lawyers.
They will appear again in Night of the Vesuviuses
In terms of personality, the Vesuvius twins are cruel, spoiled, and sadistic.