Actually use of line "Cached using Nginx Helper ..." is bit tricky.
You can disable timestamp in Nginx-Helper setting to avoid that line being added to every page. Only purpose of timestamp feature is to make it easier to debug page-caching.
The plugin itself doesn't decide what to cache and what not to cache. That you need to fo from Nginx config and I guess you are already doing that.
Purging/Cleaning are only cache related operation nginx-helper does and disabling timestamp won't affect them.
We will changes words we use to convey intended functionality in better web.
On a sidenote, I will suggest you to use responsive web-designs rather than creating and maintaing different site for mobile-devices.
Please let us know if we missed any point or anything is not clear.