She didn't start to date him because she thought he was the one who saved her in her previous life.
When she first thought that he was Van, she came to him to say thanks. Then, as they worked together, she got to know him and fall for him.
And when she told him about why she first approached him, he cleared the misunderstanding right away.
It's just that by that point, she was already in love with Hiroto, so it didn't really change anything.
Just because Van saved her doesn't mean that she had to fall for him.
And she fell for Hiroto after knowing him for several years, and not because she thought he was Van.
So he didn't steal the girl.
As far as we know, she might have have fallen for him even if Van had been there.
(If you're wondering why she didn't try to find the real Van, she just assumed that he had refused Doltcorte's offer and that he had gone back to the reincarnation circle)