Experiments have been carried out to explore the reaction dynamics leading to incomplete fusion of heavy ions at moderate excitation energies. Excitation functions for $^{168}\mathrm{Lu}$${}^{\mathrm{m}}$, $^{167}\mathrm{Lu}$, $^{167}\mathrm{Yb}$, $^{166}\mathrm{Tm}$, $^{179}\mathrm{Re}$, $^{177}\mathrm{Re}$, $^{177}\mathrm{W}$, $^{178}\mathrm{Ta}$, and $^{177}\mathrm{Hf}$ radio-nuclides populated via complete and/or incomplete fusion of $^{16}\mathrm{O}$ with $^{159}\mathrm{Tb}$ and $^{169}\mathrm{Tm}$ have been studied over the wide projectile energy range ${E}_{\mathrm{proj}}\ensuremath{\approx}75\text{\ensuremath{-}}95$ MeV. Recoil-catcher technique followed by off-line \ensuremath{\gamma}-spectrometry has been employed in the present measurements. Experimental data have been compared with the predictions of theoretical model code PACE2. The experimentally measured production cross sections of \ensuremath{\alpha}-emitting channels were found to be larger as compared to the theoretical model predictions and may be attributed to incomplete fusion at these energies. During the analysis of experimental data, incomplete fusion has been found to be competing with complete fusion. As such, an attempt has been made to estimate the incomplete fusion fraction for both the systems, and has been found to be sensitive for projectile energy and mass asymmetry of interacting partners.