Absolute atomic oxygen densities measured space resolved in the active plasma volume of a COST microplasma reference jet operated in He/O2 and driven by tailored voltage waveforms are presented. The measurements are performed for different shapes of the driving voltage waveform, oxygen admixture concentrations, and peak-to-peak voltages. Peaks- and valleys-waveforms constructed based on different numbers of consecutive harmonics, N, of the fundamental frequency f0 = 13.56 MHz their relative phases and amplitudes are used. The results show that the density of atomic oxygen can be controlled and optimized by voltage waveform tailoring (VWT). It is significantly enhanced by increasing the number of consecutive driving harmonics at fixed peak-to-peak voltage. The shape of the measured density profiles in the direction perpendicular to the electrodes can be controlled by VWT as well. For N > 1 and peaks-/valleys-waveforms, it exhibits a strong spatial asymmetry with a maximum at one of the electrodes due to the spatially asymmetric electron power absorption dynamics. Thus, the atomic oxygen flux can be directed primarily towards one of the electrodes. The generation of atomic oxygen can be further optimized by changing the reactive gas admixture and by tuning the peak-to-peak voltage amplitude. The obtained results are understood based on a detailed analysis of the spatio-temporal dynamics of energetic electrons revealed by phase resolved optical emission spectroscopy (PROES).