From http://www.w3.org/TR/html5/browsers.html#offline
5.7.7 Expiring application caches
As a general rule, user agents should not expire application caches,
except on request from the user, or after having been left unused for
an extended period of time.
Application caches and cookies have similar implications with respect
to privacy (e.g. if the site can identify the user when providing the
cache, it can store data in the cache that can be used for cookie
resurrection). Implementors are therefore encouraged to expose
application caches in a manner related to HTTP cookies, allowing
caches to be expunged together with cookies and other origin-specific
data.
For example, a user agent could have a "delete site-specific data"
feature that clears all cookies, application caches, local storage,
databases, etc, from an origin all at once.
About the Google Page Speed warning, it is most likely to be on the SERVER-side.
You should take a look at your server config files, or perhaps your .htaccess files.
Related : https://stackoverflow.com/search?q=html5+cache+control
and from : HTML 5 Cache Manifest Vs. Etags, Expires or cache-control header
Here are some resources that will get you started: