Satoru is the AU version of Blue/Green Oak and is the boyfriend of Eva Iden'no aka Leaf. He is very similar to his canon counterpart with some differences due to the nature of the AU, but fundamentally is still Blue/Green Oak from the Kanto games.
I do not play Blue/Satoru as having been abusive towards his Pokémon, merely strict and pushing his team to the edge of their limits, but never passing them. The Pokémon Adventures/Pokémon Special manga even evidences that he's strict, but not abusive, I would assume his game counterpart is exactly the same in that regard.