Did DPC exaggerate mc's reaction on Josy + Maya in chapter 4 just to have a common ground when mc and Jade later talk about their respective relationship problems (Jade-Stephen and mc-girlfriend) which finally leads to mc's long night with Jade?
I do think the game intentionally exaggerates the MC's response to Maya/Josy, but I don't think it was
just for the Jade scene.
I think the main goal was simply to sell "The Twist." If Josy's sudden arrival merely causes the MC to start a long series discussion with the girls, that undercuts the surprise of the reveal. If he instead harps on about his hurt feelings and betrayal before storming out, that lets the surprise intensify the drama. It also increases the stakes for those of us still rooting for the MC to get together with one of both of them.
The other main benefit is that it forces the MC into new situations. He might have wound up crashing with Derek for a few days if he and the girls had behaved more civilly, but it's very unlikely he would have asked Sage or Bella to take him in.
Things like Jade's soul bearing or Jill's funny face are, IMHO, side benefits that DPC was wise enough to take advantage of, but could have happened in other ways just as easily.