To configure Informant to do this you must first go into the device settings, privacy, and make sure that the Informant slider is set to the on position.  Repeat for reminders and contacts.

Then in the Informant settings, sync accounts move the calendar app and reminders app sliders to on.

This opens up the communication between Informant and iOS database.

Exchange and iCloud syncing have to be configured in your device settings and the data will need to be visible in your devices native calendar and reminders applications in order to be visible in Informant as Informant is using this database instead of its own for data to display.  The device handles the syncing and storage of the data and Informant, in this configuration, is the user interface for the data.

Direct entry with Siri is done much the same way, when you speak in an event or task it is saved to the iOS calendar or iOS reminders database and is then shared with Informant.

Data being used in Informant via any of these methods is not syncable via Informant but rather can only be synced by the device since it is the devices database.