A fully three-dimensional Primitive Equations simulation is performed to "reunite" the local equatorial dynamics of the subsurface CounterCurrents (SCCs) and thermostad with the large-scale tropical ventilated ocean dynamics. It captures (i) the main characteristics of the equatorial thermostad, the SCCs location and their eastward evolution as well as the Potential Vorticity budget with its equatorial homogenization to zero values; (ii) the large-scale meridional shoaling of the thermocline equatorward. It supports that the two-dimensional Hadley cell mechanism proposed by Marin et al. (2000) is a candidate able to operate in a fully three-dimensional ocean. The main difference between the 2D Hadley cell mechanism and the oceanic 3D case is that for the 3D case the large-scale meridional velocity at zeroth order is geostrophic, while the cell mechanism is a next-order, small-scale mechanism. A detailed budget of the zonal momentum equation is provided for the ageostrophic dynamics at work in the SCCs. The mean meridional advection and the Coriolis term dominate, discarding the possibility that lateral eddies play a major role for the SCCs creation. A 3-1/2 layer idealized ventilation model, calibrated to the 3-dimensional simulation parameters, is able not only to capture the tropical density structure, but also to isolate the main controlling factors leading to the triggering of the equatorial secondary cells with its associated jet and thermostad, namely the shoaling of the equatorial thermocline due to low potential vorticity injection at distant subduction latitudes. It is also shown that equatorial recirculation gyres play a quantitative role which may be of the same order of magnitude as ventilation from higher latitudes.