I don`t think there is such a thing has a west coast style of hitting. Never heard of it and I have been all over. I would say that people often refer to a certain style based on a school, an area, a team because most of their hitters have a similar hitting style.
I know there is a softball instruction facility in Vancouver, Canada that`s called West Coast Softball Academy. I don`t if that can be it or not.
It`s probably just a style named that way a hitting instructor referring to a particular hitting style whether be rotational, driving through or etc...
Lots of college coaches teach things about hitting that a quick review of elite hitter video would reveal to be in error. Lots of paid instructors as well. Don't know about Princeton but a kid we talked to this weekend just came back from a camp at one of her top two choices. This kid has been schooled from day one, high school and travel, how to swing a bat efficiently. At this D2 school the camp taught something like this. Photo 18 of 31, Analysis When she and her team mate asked the other campers if this didn't seem odd to them, they all answered no, it's what they had been taught all their lives. Then the college hitters did a little demo and stunk. So...west coast hitting? Who knows?