Potential energy fluctuations in the liquid phase of small atomic clusters (e.g. Ar-13) have been seen to have long-range temporal correlations. This is manifest in a power-law decay for the power spectrum, which has a characteristic 1/f dependence on the frequency,f. (More precisely, the dependence is 1/f(alpha), with alpha approximate to 1.) In order to understand the origin of this behavior, we study the melting of mixed rare-gas clusters Ar12Xe and Xe12Ar (via molecular dynamics simulations). Substitution of atomic impurities introduces widely differing time scales in the dynamics, and we show that long-lived memory-effects have their origins in hierarchical relaxation processes arising in the motion of the atoms from the surface to the core and vice versa.