boards are 4" wide or so?
I always use the miter guage for tenons against the sacrificial fence. There is no safety issue since the cut is open on the end over the blade. It does assure the workpiece stays 90 degrees to the blade/fence. I would look at the fence to see if it is attached securely to the main fence. I know you have a new Biesemeyer fence so, maybe you are using a "U" shaped sacrifial fence that caps over the Biesemeyer. How snug is that fit? A strip of tape will make it a snug fit.
Is there any lateral play in the arbor? Can you move the dado set in or out when the power is unplugged. That should even itself out under power at any case.... just looking for possibilities.
It the arbor nut securely fastened?
Is there a paper washer or other compressable piece in the dado stack?
I'd get several scraps and make some test pieces to recreate the condition. Keep the same face down for a test and flip it around.
Then turn it over and make the opposite side cut...any difference?
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)