Hi Joyce! I really hope you'll reconsider your decision to remove our plugin.
Local caching happens with any site you visit on the internet. The way local caching is handled depends on browser settings. If one of your readers visits your site and opens a post they haven't yet viewed, our apps will load perfectly for them.
And if you are using a caching plugin, what it does is cache a static version of your site that unfortunately, will not be automatically updated after installing and configuring a new plugin, but this is not by fault of the Shareaholic plugin.
Caching plugins are really awesome tools to help speed up your site and are recommended for a better WordPress experience, especially for established sites, but they basically function as a way to use backup copies of your content to reduce the server load.
After installing new plugins or making any changes within your blog, you should always clear the cached data in any caching plugins to make sure you are purging the static copies so that new ones can be created that contain the changes made.
And if you only need to worry about local caching by your browser (if you do not have a caching plugin installed), visiting a URL you haven't yet opened or one you haven't visited in a while (since the last time your cache was emptied by you or the browser) will load the page source, complete with our apps in the spot you specified for them to render.
We cannot control caching, except internally inside our own plugin resources. I'd love to welcome you back into our publisher community. I think you'll really enjoy using Shareaholic. If/when you do reinstall, just make sure to empty your caches after configuring your settings and you'll be all set! :)