The curse is cast by the Sea Witch and the Snow Queen. In Ezmia's case, they plant the idea of conquering the Otherworld in her head, which leads to the events of The Enchantress Returns.
In Alex' case, the witches want to use and manipulate Alex into a weapon to take over the Otherworld. She is to break down the Otherworld's defences so the witches can take over. Alex proves to be much more powerful than Ezmia and manages to break the curse's hold on her. The Sea Witch and the Snow Queen then suggest that all the other witches join them to curse Alex with all of their combined power.