I've posted an answer on Meta Stack Overflow four hours ago. Appears it was my twentieth answer with the discussion tag, so I got the discussion tag badge. I was surprised because the tag badges are usually awarded around UTC 3:00 AM. Well I thought, maybe the script was too late.
Then it got downvoted, and to my greater surprise, my tag scores soon went down too. Again, I'd expect it to happen at UTC 3:00 AM.
Has something changed recently?
The tag scores have already updated twice since (current state), which seems to be inline with the downvotes I was getting. Now I've removed the answer, let's see if I get the badge revoked and the scores updated again.
So yes, the score definitely updates now more often.