If there was no salt in the database, it looks Tumblr used a secret "pepper" (https://en.wikipedia.org/wiki/Pepper_(cryptography))? Why wouldn't they include a salt as well? Or did the database dump just not have the salt column?
It's absolutely clear that Tumblr did not use a pepper to create the dumped hash values in the article. Multiple users had the same hash, and most of those users had the same password as each other on another site.
Or are you saying that the exact same hash was found in multiple separate database dumps? I didn't see any indication of that in the article.
"The pepper is randomly generated for each value to be hashed (within a limited set of values), and is never stored. When data is tested against a hashed value for a match, this is done by iterating through the set of values valid for the pepper, and each one in turn is added to the data to be tested (usually by suffixing it to the data), before the cryptographic hash function is run on the combined value."
In case you're interested, that is the same scheme as the one used by JoeyH's keysafe[1].