Yep. The Responsibilities section on the app is currently frozen and cannot be changed by a host. Editing the listing on either the app or the website edits the same material in the new Pet Responsibilities and Home Tasks sections but only the web version currently displays that material. The app version only displays the single Responsibilities section that existed 2 days ago. It took me an hour to figure out what was where. It’s all very confusing at the same time THS went radio silent on this “minor” change.
In @Lokstar’s example, the host did not have anything in the single Responsibilities section 2 days ago before it was it was encased in carbonite à la Hans Solo 2. Since then, the host has edited their listing adding stuff to Pet Responsibilities and Home Tasks that can not be seen using the app. Trying to explain this to new hosts is probably counterproductive; they’re likely going to think you’re a few fries short of a happy meal.