Yeah they both think they've been forever separated. There's no reason for them to assume otherwise yet. It's sad but also potentially touching to see two people fall in love all over again without realizing it. Even though they should be "enemies," just being near each other for a couple moments has reminded them of each other and made them start connecting.
already making connections to eachothers' past life... very cute, shows how much they meant to eachother that they still wish the other the best in another world (but actually the same world)