How to strong winds cause baroclinic intensification in the upper ocean?
Strong upwelling-favorable winds (like the ones described) cause coastal upwelling in the following manner: 


Winds in these systems flow parallel to the coast (with the coast to the left in the northern hemisphere or to the right in the southern hemisphere) and generate upwelling dynamics. 
Surface Ekman balance is setup (in deep enough waters) with water transport being to the right (left) of the wind in the northern (southern) hemisphere. The result is a deficit along the coast that requires a compensating flow in the deeper part of the water column bringing usually colder waters to the surface.


 Source Commons Wikipedia.


The resulting density (mostly controlled by temperature in these systems, but sometimes affected by salinity in areas with river influences) shows a strong horizontal gradient. A strong horizontal gradient in density is the definition of strong baroclinicity. That strong gradient can even be visible in a temperature front when the thermocline reaches the surface (SST image below). 
Additionally, the density gradient can establish a thermal wind balance that results in a coastal upwelling current jet flowing in the same direction of the wind. The horizontal gradient in density is proportional to the vertical gradient in velocity
$\mathrm{{\delta\rho\over\delta x} \propto {\delta v\over\delta z}}$ . As velocity is zero at the bottom, this results in a strong velocity near the surface. This is what we understand as "intensifying the baroclinicity in the upper layer".


 Source: Satellite image of SST showing multiple upwelling centers and cold filaments off central California (Courtesy of E. Armstrong).