Connected to Time capsule from iOS devices
There is currently no native way to view files on a network share from iOS devices.

You will need a third party program such as FileBrowser or Files Connect to browse and view files stored on the Time Capsule.

Files Connect seems to be the most feature complete of the two examples having both Google integration and Dropbox support; they even show a Time Capsule connection in their promotional image as below:



I would also think it very unlikely that any program available on an iOS device will be able to view files stored in Time Machine backups if that is one of your requirements.

Please note the links above are to the apps in UK App Store.