Picture of the inconsistency
Electric mining drills and inserters do not exhibit this behavior and will output to a consistent lane in all rotations. Because almost nothing else in Factorio changes behavior due to changes in rotation, I would consider this a bug.
To be consistent with the behavior of electric mining drills and inserters, I think the behavior when the burner mining drill is facing north is the correct behavior, and the behavior during the other 3 directions should be changed.