That's not perfect btw, many apps today are using websockets (e.g. https://github.com/daltoniam/Starscream) to connect upstream and they bypass iOS/Android proxy settings entirely with no way for http based mitms to see that traffic.
I've found this developer to be trustworthy, has a good track record with his git app. I'd be surprised if he would make this claim if it were untrue... it could easily be proven wrong by anyone using Charles proxy.
You could use something like Charles for iOS to see that it doesn't connect to anything except the servers you configure.