Currently only actions on Local Notifications are handled. We, as Titanium Developers, can display Remote Notifications with Actions, but a click on one of the buttons is never received by the app.
In TiApp.m the following is implemented for Local Notifications
A similar AppDelegate function has to be implemented to handle Actions on Remote Notifications
I reckon that the implementation can be similar to
With in addition a key in the event details which action was triggered.