Think of "open" more as "do something with". When you set Firefox to use the default applications, it defines what program will handle the file. Handling the file will not necessarily mean "open".
If you want to open a file found online, it is first downloaded to your computer which is where the application uses it. Once it has been downloaded to a temporary location, Windows, for your convenience, asks you whether you want to just save it to a location of your choice or open it. If you actually want to go to the bother of opening it, it gets passed to the default or specified application.