Yes, several sites already uses Amazon S3 to store the content. 

To use Amazon S3 storage configure it (as you already did) and set default storage engine in Studio > Settings > System > Storage > Default Storage engine (as I see you did it as well)

I would suggest to configure S3 storage just after UNA install while there is no any content uploaded to the site, since existing content will not be transferred to S3. Also Storage engines which have existing content will not use S3 storage.

It maybe you have some existing content - this is the reason it wasn't switched to S3, please try to install clean UNA site and configure S3 before uploading any file.