The instanteneous crossectional area of the specimen decreases during tensile test. slightly small decrease under homogenous deformation and much larger decrease when the specimen starts to experience localised deformation and as aproaches necking.
As for compression the crossectional area of the specimen in contact with the tools is some what hindered from expansion due to friction. However parts of the workpiece located further away from the tools will not experience the same frictional force and therefore be free to expand. The result of this will be a crossectional area which increases away from the tool contact and reaches a maximum value at the equitorial region of the work piece. ( Just imagine the appearance of a cylindrical billet which is compressed to half its original height)