Step-by-step for moving large site uploads to S3?

It looks like this applies to all posts on the forum. I had a look at several raw/unbaked posts and the images are all referenced like this:

![IMG_20150512_182321|690x388](upload://d5tlLS5VtcU7PAaOgzFsROaB6vc.jpg)

When I look at the uploads table, the entries all have a URL of the form:

//jl-discourse-uploads.s3.amazonaws.com/original/3X/8/a/8a560451dcba13a7f9d4545368c078e82ef890ac.jpeg

Which should be correct, no? So, it almost looks as if something in Discourse is adding the https://forums.jag-lovers.com part on the fly?

Do I have to rebake all the posts?

Thanks, @mmayo!

Thanks,
Gunnar