I have been able to reproduce this on an iPhone 4S running iOS 7 only. We don't have an iPhone 5 to test on right now, but I believe it's the same issue. I was unable to reproduce on iPad, nor on the iPhone with iOS 6, or on any Android device at all. So it appears limited to iPhones with iOS 7 only.
As far as I can tell this is not a Construct 2 bug. It is simply the unfortunate way that Safari on iOS 7 works. When on the iPad the UI bars are locked in-place and never come and go. However on the iPhone Safari iOS7 implements a fullscreen-when-in-landscape mode, unless the user touches near the top or bottom of the screen, in which case it brings the UI bars back. Worse, the UI bars float over the game content area. So Safari is telling the game that the available size of the window is an area including that which the toolbar covers. Therefore the game is taking the correct size that it is being told to, but Safari then covers up part of the game with its own UI, creating the "cut off" appearance.
We are not aware of any technical means by which we can work around this. We understand it is also affecting many other developers and publishers using other HTML5 engines (see: http://www.mobilexweb.com/blog/safari-ios7-html5-problems-apis-review, http://www.html5gamedevs.com/topic/1436-ios7-is-going-to-break-your-games/). However there is one workaround the user can do: rotating the device to portrait then back to landscape restores the fullscreen view, without cutting off any of the game with toolbars. However as soon as the user touches near the top or bottom again, the toolbars come back and the same problem occurs.
A way to make the problem less likely to occur is to move all buttons and controls closer to the middle of the screen. Some of your buttons, such as the "Continue" button on the Storyline layout, sit mostly within the bottom area where a touch brings back the toolbars. If it were moved closer to the middle of the screen, touching it would probably not bring the toolbars back; unfortunately, if the user even accidentally touches near the top or bottom, or the gameplay requires it, the toolbars come back again and the user must go portrait then landscape to remove them again.
Since we are not aware of a good way to work around this from our engine, all we can recommend is that you and all your affected sponsors and publishers petition Apple to fix the problem. If they implemented the Fullscreen API, which Construct 2 has supported for a long time, the problem would almost certainly be resolved. This would allow you to explicitly switch in to fullscreen using the Browser object's 'Request fullscreen' action, which is supported in Chrome for Android and a few other platforms. This allows fullscreen (and in some cases, orientation-locked) display without ever showing any toolbars, unless the user performs a specific gesture (e.g. swipe down from top in Chrome for Android). So perhaps implement fullscreen support this way, testing on Chrome for Android, and petition Apple to add fullscreen API support. If they do and your game already supports it then it will be fixed as soon as Apple adds support.