From what I understand, they reincarnated by their own strong desire/wish for the characters. Emi for Remilia's happiness, as for the other one (I think her name was Rina) the one possessing Pina wanted to destroy Remilia. Which in turn, causes Emi to went on a soul coma (during the banishment scene),it let Remilia (the true Remilia) took reigns for the first time (at this point, she knew just from observing Emi's Actions also via her memories, that she cared for her so much and was the Only person with true affection for her as a person.) and that's when Remi decided to take revenge because of their actions, she lost the person she cared for the most and taught her love. Hence why she tends to refer herself as Emi (Remilia) due to the fact she's acting like how Emi would've act if she's still here.