Generally, cold working like rolling process causes the micro-structure and dislocations to move and re-arrange in direction of rolling. During this movement, dislocations stuck and lock to each other and further deformations become more difficult and hence, strength and hardness of the material increase (strength and hardness are directly related through for example Tabor equation).
Your observation could also be explained from the view point of texture. After cold-rolling, the metal has developed a preferred orientation in which certain crystallographic planes tend to orient themselves in a preferred manner with respect to the direction of maximum deformation. This creates what is called very high planar anisotropy while lowering seriously what we call average normal anisotropy. It is the result of this high planar anisotropy that causes discrepancy in measured Mechanical properties of the rolling direction to the normal direction. However, if the rolled sheet is annealed, planar anisotropy can be eliminated or drastically reduced.
I am facing a similar issue, I think most of the researchers looking at the cross-section when they do hardness measurements but perpendicular to that when they do strength measurements through the tensile test. in my opinion when we do hardness or a tensile test we should do it in the same orientation to be able to correlate the results.