
If you have multiple player types on your system, it's recommended to opt into Background Updates (update option = Allow Adobe to install updates). Therefore, IE launched and the update for NPAPI plugin was downloaded and installed. In your case, NPAPI plugin for Firefix needed to be updated, and IE is the default browser. Due to technological limitations, the default browser is launched, instead of the browser that corresponds with the player type that needs to be updated. If an update is found, a registry entry is created to display the Notification Update dialog window upon system login to update that player type. This happens when the player periodically checks for an update.

ActiveX for IE, NPAPI for Firefox, PPAPI for Chromium-based browsers) is updated at a time. For Notification Updates, only a single player type (e.g. The behaviour you experienced is normal and how Notification Updates works.
