Here's my latest issue with modeling Asians, including a small insight I've had regarding making targets work together.
I think it is a weakness of the built-in modeling tools that they try and isolate the treatment of the back of the jaw and the front/chin, in the case of the Asian model this makes it impossible to produce a straight jawline with any prominence. With the Caucasian model you can always find a balance between prominence and chin width, but with the Asian model you can't because the angle of the rear half of the jaw is greater than what you can produce by adjusting chin width.
If the jaw width, chin width, and chin prominence adjustments all adjusted the full length of the jaw then they could be adjusted independently while maintaining a straight jawline. I encountered the same thing with my brow ridge adjustment target, initially I only adjusted the mesh near to the brow ridge, which worked fine when with the default forehead shape, but then when I made a second target to produce a flatter forehead I ended up with a bend/corner when I used the two together. By having the brow ridge target adjust all the way to the top of the forehead this problem went away.
Here are the default models for male Caucasians and Asians:
Note the difference in angles between the back and front of the jaw for the Asian model.
You can see the difference clearly when you add some chin prominence:
With the Caucasian model you can usually find a combination of prominence and chin width to produce a realistic straight jaw:
But with the Asian model no amount of chin width adjustment will produce a straight jawline:
I'm working on a jaw width target that preserves a straight jawline: