We investigate the transient dynamics of a short overdamped Josephson junction with a periodic driving signal in the presence of colored noise. We analyze noise induced henomena, specifically resonant activation and noise enhanced stability. We find that the positions both of the minimum of RA and maximum of NES depend on the value of the noise correlation time tau_c. Moreover, in the range where RA is observed, we find a non-monotonic behavior of the mean switching time as a function of the correlation time tau_c.