Searching is tricky. Things aren’t always labelled the way you expect. In this case, I had to track back to the commit that removed the function from imgICache.idl.
A little background on cache. Everything, html pages, images, etc is all cached on disk (unless it is private browsing, cache is disabled, etc.). There is also an in-memory cache for things that can’t be written to disk for privacy or policy reasons, but it is very rarely used. When you load something, this is the first place to look, then possibly a check over the web to see if a newer version of the resource is available. If you code your own XMLHttpRequests then you can force the timestamp check, or even completely override the disk cache. Possibly in your case, you are working with images that you obtain yourself and are not even in the disk cache? Perhaps you have your own disk cache?
As you’ve no doubt found, replacing an image that is displayed by Firefox with a different image at the same URL does not result in a change in Firefox. Images are decoded and cached in a special image cache (actually now two image caches, one for private browsing), entirely separate and in addition to the standard document caching. This is manipulated using imgICache, and now imgITools, but only in a very limited way.
I’m not so familiar with the new worker Cache Storage objects. They are new and should enable web workers to maintain their own semi-persistent stores of data. So far as I know this shouldn’t affect the existing caching arrangements, but maybe I’m missing something.