Safari should support Service Workers[1], because they allow you to safely intercept and modify navigation and resource requests, and cache resources in a very granular fashion, securely and on a different thread to your app JS. This is great for performance and offline/spotty reception.
The Web App Manifest[2] is the file that allows developers to "appify" the site, by prompting the user to add to their home screen (only once they hit a certain usage rate), show a splash screen etc. But that's a nice to have compared to Service Workers.
[1]: https://developer.mozilla.org/en/docs/Web/API/Service_Worker...