Earlier quoted context omitted.
Individual Tumblr blogs get to decide whether example.tumblr.com is "only visible to logged-in users." If they turn on that setting, the site 1. forces you to log in, and 2. renders the site inline as part of the Tumblr dashboard SPA. If you don't turn it on, though, your Tumblr blog is a public/static website indexable by Google.
Importantly left out here is what the default is. It sounds like the default is must log in - I can't imagine how many tumblr users would choose to only have logged in viewers. I've left a while though so feel free to correct that.
There is also, above and beyond that, the ability to make a blog private, by setting a password to access it. A blog with a password is still rendered out to a static site, though, strangely enough; just one with the equivalent of an .htaccess password-gate behaviour.