Why is compensatory negative supercoiling generated in a positively supercoiling ccDNA?
For a piece of topologically constrained DNA, Lk is constant. Since Lk = Wr + Tw, if you increase Wr in one area, it can be compensated by decreased Wr or Tw in an adjacent area. You may ask why the unwinding is concentrated in the adjacent region and not spread throughout. This is explained in the paper you link to:


  Although any superhelical strain generated by DnaA-mediated wrapping would be expected to spread throughout the topological domain that contains the origin, it may preferentially affect the nearby DUE, which is unstable and prone to spontaneous unwinding.


The DNA unwinding element (DUE) is unstable because it is AT rich:


  …the opening of individual AT/TA base pairs in the three DUEs investigated differs from that of GC/CG base pairs in at least two respects. First, the opening of AT/TA base pairs is significantly more favorable, kinetically and energetically, than that of GC/CG base pairs. Second, the opening of AT/TA base pairs is affected by long range effects of the DNA base sequences, whereas the opening of GC/CG is insensitive to the base sequence beyond that of nearest neighbors. The first difference confirms the earlier proposal that the high content of AT and TA base pairs is necessary to lower the stability and enhance the dynamics of the three DUE sites. The second difference suggests that the sequences of these AT and TA base pairs have been selected by evolution as a means to modulate the energetic stability of the three DUE sites according to their location and function in the origin of DNA replication.