Projects that I had joined before discovering (and using) BAM! don't appear under "My projects." Is that the way it is supposed to work?

Yes, you have to attach all your projects to the account manager manually. But, it's pretty easy if you're using the same account information that you are with BAM. Then, you can just go to the "Sign-up for projects" page and click the magnifying glass (Find account) icon next to the appropriate project(s).