We numerically investigate the change in synchronization property in different frequency components associated with laser dynamics, which is termed dynamics-dependent synchronization, in two mutually-coupled semiconductor lasers. We introduce an optical amplifier to implement asymmetric feedback, and we change the feedback strength of one of the two coupled lasers to observe dynamics-dependent synchronization. In-phase synchronization is observed for the original signals, while anti-phase synchronization is found for the low-passfiltered signals, in the presence of low-frequency fluctuation dropouts. We analyze dynamicsdependent synchronization by observing temporal changes in the short-term cross-correlation and the local optical frequency detuning.