I am trying to work this out as I go. I must say it is poorly communicated by apple themselves. But I think there won't be a need for an app on iOS. If you can access iCloud drive from any app, say a pdf annotator or whatever, perhaps there is no need for a stand alone app.
Of course there is no standalone app, there was never going to be a standalone app, and any misunderstanding is your own and not Apple's fault.
I have already replaced Dropbox with iCloud Drive, however I'm using Yosemite, where the file management aspect actually comes into play. It's also available through iCloud.com, but only in beta form at the moment.