If you want all files to be served via S3 then you need to configure it right after UNA installation.  If you do it later then some files are hosted locally and some on S3. Files which are already stored locally will be stored locally as well.

As an example, if you upload some file to Albums module before configuring S3 then all files in Albums module will be hosted locally even after S3 configuration. If module has no files uploaded before S3 configuration then after you configure S3 then albums storage is converted to S3. The same is vice versa - change default storage from S3 to Local.

For the custom subdomain please refer to Amazon docs, "Customizing Amazon S3 URLs with CNAMEs" section:
http://docs.aws.amazon.com/AmazonS3/latest/dev/VirtualHosting.html