I'm going to guess the first prince is also a reincarnator like Ash. He seems to already know that Elise egging on the second Prince is a reincarnator, as well as that Fine is supposed to be the saintess. Fine also didn't recognize him and she basically alluded that he appeared to be a different person. If the first Prince is like the main character Ash, that could mean that early on he didn't have any memories of his previous life till after he encountered Fine, so his personality and demeanor now that he has his previous life memories, makes him seem like a different person when he first met Fine when he didn't have previous life memories.