A post on the Tumblr staff blog said:
“We have just released a very important security update for our iPhone and iPad apps addressing an issue that allowed passwords to be compromised in certain circumstances¹. Please download the update now.If you’ve been using these apps, you should also update your password on Tumblr and anywhere else you may have been using the same password.”
The blog post appears on the timeline of users when the open up the app, it looks like they are really keen to get this issue wrapped up. There is no update for Android users who remain unaffected by the security issue.
So, if you’re one of the people writing one of the 900 posts published every second on Tumblr change your password as soon as you can!