I made few test today with Firefox and Chrome browsers working at the same time.
Pages opened in Firefox do not show as cached when opened in Chrome afterward, and vice versa.
Furthermore it seems that Firefox delivers cached files from cache/ folder, file Chrome delivers files from cache/supercache folder (I inspected them manually)
Both browsers show the cached files on reload but they are coming from different folders.
Page load in FF->cache file is created in cache/ and only FOLDER is created in cache/supercache
On reload cached files is server from cache/, still only folder in cache/supercache
Cached page ends with:
<!-- Dynamic Page Served (once) in 0.301 seconds -->
<!-- Cached page served by WP-Super-Cache -->
After that I load the page in Chrome. Uncached page is showed. Cache file is created in cache/supercache folder.
Next time page is loaded it is cached, ending with:
<!-- Dynamic Page Served (once) in 0.406 seconds -->
<!-- super cache -->
Test performed on two sites with no other plugins turned on. Strangely on your site it seems to work fine.