I had to give up using DownloadManager as downloadUrl adds an extension to the URL that Safari does not appreciate when handling blobs (and isValidUrl does not accept the blob: protocol).
Also, as we don't know the content type of the attachments, and because Safari does not implement the "download" attribute on anchor tags, it tries to display the file in the current page, which generates errors. Opening the attachment in "_blank" is the cleanest way I can find to deal with that. It works fine in Firefox and Chrome though.
What do you think?