Phone, Reminders, and Maps use a different 3D-Touch Peek UI allowing to select an action in one go. For instance, force-press on a reminder and select "Remind me on a day" in one go, without releasing the finger. It also differs visually from standard 3D Touch previews using the UIViewControllerPreviewing
API as it displays a custom icon alongside left-aligned text.
I couldn't find a way to do this using the official API. Did I miss something or is this a private API indeed?
I asked my question on the Apple Developer Forums as well and received this reply from Apple:
Currently there is not public API to do these things. Please file bug reports if this is something you want to do in your app, and include specific details of what you're looking to do.
So it's currently not possible using the official SDK. I filed this enhancement request radar and I encourage you to dupe it if you need this, too!