We have investigated the spontaneous formation of the regular quadrilateral defect array in cholesteric emulsions, composed of water, surfactants, and cholesteric liquid crystals. Both at the substrate surface and at the sulfactant-coated droplet surface, a homeotropic anchoring is enforced to the adjacent liquid crystal. We observe nucleation of numerons point defects, in the cholesteric planar texture immediately after termination of shear to the emulsion, which leads to the formation, of the regular defect array. Two distinct steps were identified in the formation process; the first step is the nucleation and growth process of point defects, and the second step is the rearrangement process of point defects to the regular defect array.