So it's a longer exposure on the second shot. Is that what you notice as being consistent?
I've not yet seen this on my D4, that is to say variation in exposures running at 10 fps and I have tested it quite a number of times on people (both stationary and moving). However I've not looked specifically at the first two frames. What happens after the second frame, does it stay brighter than the first frame?
I don't think it is changing light. The quality of the light in the images looks identical and clouds don't move that fast. Also the matter of the speed of light is not important because so many other things would affect the light other than how fast the light is traveling itself (like clouds).
I would run the tests on a white background....pure white and put the camera on a tripod with spot metering, then with matrix metering and compare them over a long cycle of maybe 20 frames using either A mode or manual mode. My guess is that if you are using matrix metering, the way that the computer is accessing the library of possible metering outcomes varies slightly as the frame is being sampled, similar to what you see with how the autofocus behaves in terms of sampling areas sometimes before reaching the face. At high frame rates the CPU has to keep up with both autofocus and metering. Also with an electromagnetic shutter, there are intermediate shutter speeds apart from the usual ones we are familiar with so the meter might be making slight adjustments based on this white person with bright white shirt against a white background. The meter is struggling to achieve a balance approaching 18% grey and with so much white it will be trying to balance the variables around a hovering ideal setpoint for that particular set of intensity values across the frame.