You should be able to get this working. I have the NI M32, which is similar to the A61, exactly the same controls, it just has 32 mini keys instead of 61 full size keys. I'm guessing the underlying software is almost identical. My M32 is able to control a small amount of DAW functionality with no issues. You may want to confirm the following to get it working on your computer:
Please make sure you have the latest firmware for your A61, and the latest version of Komplete Kontrol, which is 2.3.
Once Komplete Kontrol is installed, you should run the stand-alone version of Komplete Kontrol and configure that to work with the A61.
Once that is working, go into the preferences for CbB . Under Midi Devices, make sure Komplete Kontrol A DAW is present and checked in both the input and output categories, and make sure Komplete Kontrol A61 MIDI is present and checked in the input category. Then, under Midi Control Surfaces, in the list of connected controllers, you should have a Mackie Control with input and output of Komplete Kontrol A DAW. The inputs and outputs for the controllers often get jumbled, especially if you start CBb prior to all of the controllers being connected and turned on. If need be, straighten these out. If you don't have a Mackie Control in the list, add a new controller using Mackie Control and set its input and output to Komplete Kontrol A DAW. Save these settings. Then, for good measure, close CbB and restart your computer.
When you restart CbB, make sure the A61 is in MIDI mode. If the PLUG-IN/MIDI button in the upper right is lit at all, you are not in MIDI mode. The PLAY, REC and STOP buttons will also be unlit. To go into MIDI mode, press shift and the PLUGIN/MIDI button. When you release both buttons, the light should go out in the PLUGIN/MIDI button, and turn on in the PLAY, REC and STOP buttons on the left. The A61 should now have the following functionality:
PLAY, REC and STOP will work as expected.
The 4-D encoder knob on the right will scroll the timeline when turned clockwise or counter-clockwise, scroll tracks when nudged up or down and scroll track parameters when nudged left and right. This is assuming that, between the track view and the console view, the track view was the last one "touched". This corresponds with the top to bottom arrangement of tracks in the track view. If the console view was the last of those two views to be touched, the up/down/left/right behavior is reversed to correspond with the left to right arrangement of tracks in the console view, as long as the console view is visible. If the console view was last touched, but is not visible (it is in the multidock and a different view is selected there), left/right/up/down does nothing!
Hope this helps!