I think there's a few options here. One option would to be put a delay on the observable emitting from the cache, but assuming that's used elsewhere that's a bad solution.
Another option would be to creating a window whose time bucket is the minimal animation time you want. That could delay the network case by some amount of time though.
Ultimately I think you'd need to be able to operate on the cache observable directly. If you have an abstraction layer that makes that challenging, it might make more sense to just have some logic enforcing a minimum amount of time for the progressbar to stay alive.