The tl;dr is that you can run into trouble on the iOS platform if you don't enforce a strict 1:1 chain of cause/effects and are very careful about the timing of adding new links to the chain.
This library doesn't appear to do that, and they appear to consider this a feature, and actively push you in that direction. For example, a bullet in the readme is that tasks are "fully composable" and another bullet point discusses adding new tasks to the tree on-demand. These can work on some platforms, but iOS isn't one of them, and so this really reads like someone familiar with JS or .NET trying to add "missing" functionality to iOS without considering why these patterns are not generally used on iOS. Plus, it's trying to achieve API similarity with Android, which is a code smell.
So I would really advise against using this library, at the very least use it a in a superficial way that would be easy to tear out later. If you really want to do this promises thing, I would push you toward Reactive Cocoa, which I am also skeptical about but it's been around much longer, seems to have a much more mature API, and I know at least some smart people who've used it successfully.