A green tire disposed on a toroidal support is introduced into a vulcanisation mold. The mold is closed through axial approaching of a pair of sidewall plates acting against the sidewalls of the tire. Circumferential sectors set to operate against the tire tread band are maintained spaced apart from the tread band itself during admission of a working fluid designed to press the tire against the toroidal support. Subsequently, the sectors are centripetally approached for penetration into the tread band concurrently with a step of full molding and vulcanisation of the tire carried out through admission of steam under pressure into the tire itself.