Thank to both replies. I called China Eastern again today to see if I could get another representative, and a different person again told me that I don't need to go through customs and immigration in Shanghai because "you're not going outside of the airport." Well, I know that I'm not going outside of the airport in Shanghai, but that doesn't mean I don't need to do customs and immigration...

Their customer service really leaves a lot to be desired.

I noticed that on CTrip, this flight is billed as having a "stop" in PVG rather than a "transfer" in PVG. I do know for sure that it's not the same aircraft flying the 2 segments, though.