They use the same methods you do for accessing the data. So in reality, you can check it for yourself. As you're accessing the ACP, or viewing PII, you can check the browser cache for that PII data. In looking through my own, I only see non-PII data (images, stylesheets, etc).
I also see MY own session cookies in my local browser cache, but that is my own data... not anything that would relate to any other user's session data, etc.