If this 'fated person' is basically reincarnation of the same person to Earth, coming back and forth between the two worlds bringing the culture over each time.
It'd explain why the church here is just like Christian one, the earlier reincarnations was Christian or something like that.
And then, when they're over here, ever slowly they becomes THE fated person, the first personality.
It's nothing too sudden, just ever minor things.
Like the way they act, the words they use, slowly, subtly, and the 'dream' make them sympathize ever more to the demon king.
But then when they finally meet, the girl start to feel a strange sense of longing for him.
BUT, then she came to herself, and logically thought 'no wait, why am I suddenly in love with this guy or something when it's our FIRST TIME MEETING!?'
Then suddenly she start to notice all the subtle changes that happened, become afraid of 'who' she is anymore.
The demon king tries to call her 'old' name.
Which cause her to snap "I AM NOT HER!", blurt out her personal history, then escape.
Then he will be the one to go to her and call her name properly this time then go from there.