The output is not an HDMI signal and it's not the same as the a Thunderbolt port on a Mac as it's not sending out a display signal.
The Thunderbolt port on the camera is for the following (from page 29 of the manual):
When connected to a Mac OS X computer with Thunderbolt technology, your Blackmagic Cinema Camera can be used as a powerful solution for video capture, waveform monitoring and color correction. Regardless of which recording format you choose on the camera, the Thunderbolt port always outputs HD1080p video in the uncompressed 10-bit format which is compatible with a wide range of popular video software.
The Blackmagic Cinema Camera Utility software installer installs the Blackmagic Media Express application for simple captures without the complexity of NLE software.
Blackmagic UltraScope software is also installed for waveform monitoring of your camera during recording and playback.
Video Capture
You can also use your favorite video capture applications to capture video from the Thunderbolt port of your Blackmagic Cinema Camera. Applications include Blackmagic Media Express, DaVinci Resolve, Adobe Premiere Pro CS6 and Apple Final Cut Pro 7. The "Using Blackmagic Media Express" chapter of this manual contains detailed instructions for performing simple captures with Media Express.
Waveform Monitoring
Blackmagic UltraScope software allows you to monitor almost every aspect of the video you record with your Blackmagic Cinema Camera. The "Using Blackmagic UltraScope" chapter of this manual contains detailed instructions to help you get the most out of waveform monitoring with your camera.
Color Correction
DaVinci Resolve 9 can directly capture video from the Thunderbolt port of your Blackmagic Cinema Camera. However if you are shooting RAW 2.5K Film, it would be best to take the SSD out of the camera and connect it directly to your computer to retain all quality of the original video.Grab the manual here:
http://www.blackmagicdesign.com/support ... lse&os=macRe: Minin Monitor
As Nick said, the built Thunderbolt port on the Mac is an 8-bit output for the desktop. The Mini Monitor is a playback device for broadcast monitoring from you NLE.