Currently, the only way to install mobileconfig files are using Safari or Mail app on iOS.
To install the mobileconfig, you have some choices like:
- Put the mobileconfig files on the web and open it by Safari
- Send the mobileconfig by email and open it by Mail app
- Package (or download) the mobileconfig files to your bundle and host a HTTP server by your app, then open the localhost link by safari through openURL: function.
Or, the iOS 8 way, using the new framework Network Extension to establish the VPN connection. And after trying the ZenMate iOS app, I believe it's what they use.
You can refer following resource for installing mobileconfig file:
Downloading "mobileconfig" file from an App
Installing a configuration profile on iPhone - programmatically
Or this link for using Network Extension:
Connect to VPN programmatically in iOS 8