We present detailed numerical and analytical investigations of the nonequilibrium dynamics of spin-polarized ultracold Fermi gases following a sudden switching on of the atom-atom pairing coupling strength. Within a time-dependent mean-field approach we show that on increasing the imbalance it takes longer for pairing to develop, the period of the nonlinear oscillations lengthens, and the maximum value of the pairing amplitude decreases. As expected, dynamical pairing is suppressed by the increase of the imbalance. Eventually, for a critical value of the imbalance the nonlinear oscillations do not even develop. Finally, we point out an interesting temperature-reentrant behavior of the exponent characterizing the initial instability.