How (and why) do 3rd-party iOS 6 apps communicate to their makers when they are not the active app?
Apple documents high level functionality in an article on background processes:


iOS: Understanding multitasking - http://support.apple.com/kb/HT4211


You could look at archive.org to look at a version of this for iOS 6, but pretty much everything from iOS 7 applies in iOS 6 except for the new "background app refresh" functionality.

If you wanted a deeper understanding on how multitasking works, I would start with this section of the developer documentation:


App States and Multitasking


Without capturing APNS traffic (or using Instruments to trace the OS while it runs), it's hard to tell if 30 minute access are a result of Local Notifications or perhaps push notifications being sent from the server side causing the app to wake periodically. Hopefully this is enough to get you started on tracking things down.