There are 3 different versions of Flash Player for Windows (ActiveX for IE, NPAPI for Firefox, and PPAPI for Chromium-based browsers; Mac). The one you installed is Flash Player NPAPI plugin for Firefox. If you have Flash Player ActiveX for IE or PPAPI for Chromium-based browser's it's one of those other versions that is now prompting you to update. To confirm the versions you have installed, launch the Control Panel and navigate to Control Panel\All Control Panel Items. Click on the Flash Player item and navigate to the Updates tab. This displays which Flash Player plugin types are installed and the corresponding version. The most recent version is 22.214.171.124.
The best way to avoid this is to opt into Background Updates (update option = Allow Adobe to install updates). This option updates all installed Flash Player plugin types within 24 hours of a new version being available. The Update Notification option, which is what you appear to have selected only updates one type at a time, and can take up to 7 days to notify the user that an update is available.