Three-wave mixing of ordinary and backward electromagnetic waves in a pulsed regime is investigated in the metamaterials that enable the coexistence and phase-matching of such waves. It is shown that the opposite direction of phase velocity and energy flux in backward waves gives rise to extraordinary transient processes due to greatly enhanced optical parametric amplification and frequency up- and down-shifting nonlinear reflectivity. The differences are illustrated through comparison with the counterparts in ordinary, co-propagating settings.