In the present paper, the spatio-temporal evolution of the vorticity field in the second wake instability, i.e. (pure) mode B is investigated to understand the wake vortex dynamics and sign relationships among the three vorticity components. Direct numerical simulation of the flow past a circular cylinder in the three-dimensional (3D) wake transition is performed, typically at a Reynolds number of 300. According to the time histories of fluid forces and frequency analysis, three different stages are identified. In the fully developed wake (FDW), the spanwise vortex core is almost two-dimensional, while the vortex braid is 3D due to the dominant streamwise interaction. However, streamwise and vertical vorticities owing to the intrinsic 3D instability are already generated first on cylinder surfaces early in the computational transition (CT). The evolution of additional vorticities with the same features as mode B shows that (pure) mode B could already be formed in the late CT. In the FDW, a special sign symmetry of these additional vorticities on the rear surface is observed, which is exactly opposite to that in (pure) mode B. Similarly, the two sign laws found in (pure) mode A are also verified in three typical regions, independent of the Reynolds number, for (pure) mode B. Particularly, the mechanism for the physical origin of streamwise and vertical vortices in the shear layers is the vortex generation on the wall first and then dominant vortex induction just near the wall. The entire process of the formation and shedding of vortices with three components of vorticity is first and completely illustrated. Other characteristics of the evolution of mode B are presented in detail.