Spin orbit interactions are rapidly emerging as the key for enabling efficient current-controlled spintronic devices. Much work has focused on the role of spin-orbit coupling at heavy metal/ferromagnet interfaces in generating current-induced spin-orbit torques. However, the strong influence of the spin-orbit-derived Dzyaloshinskii-Moriya interaction (DMI) on spin textures in these materials is now becoming apparent. Recent reports suggest DMI-stabilized homochiral domain walls (DWs) can be driven with high efficiency by spin torque from the spin Hall effect. However, the influence of the DMI on the current-induced magnetization switching has not been explored nor is yet well-understood, due in part to the difficulty of disentangling spin torques and spin textures in nano-sized confined samples. Here we study the magnetization reversal of perpendicular magnetized ultrathin dots, and show that the switching mechanism is strongly influenced by the DMI, which promotes a universal chiral non-uniform reversal, even for small samples at the nanoscale. We show that ultrafast current-induced and field-induced magnetization switching consists on local magnetization reversal with domain wall nucleation followed by its propagation along the sample. These findings, not seen in conventional materials, provide essential insights for understanding and exploiting chiral magnetism for emerging spintronics applications.