This issue does not appear to be specific to ATS, apologies for the noise. I've just confirmed that Apache mod_proxy in reverse-proxy exhibits the same behaviour.
So, something else is going on here which appears to have something to do with the Expires header, or cookies, or cosmic rays, or something :) ie: browserX loads and caches page1. browserY loads page1, but for some reason the cached page1 is not served. /me wanders off to stare at more HTTP headers, ...
