A hybrid simulation code is developed to treat electrons fully kinetically by the particle-in-cell/Monte Carlo collision (PIC/MCC) algorithm, while ions and neutral species are handled by a fluid model, including a time slicing technique to reduce the computational expenses caused by the responses of various species on different time scales. The code is used to investigate a capacitively coupled COST reference micro atmospheric pressure helium plasma jet with 0.1% oxygen admixture excited by a valley-type tailored voltage waveform with a fixed peak-to-peak voltage of 400 V, and a fundamental frequency of 13.56 MHz. The computational results are compared to experiments based on several sophisticated diagnostics, showing good agreement in the electron impact helium excitation rate, the helium metastable density, and the atomic oxygen density. The spatio-temporal electron heating dynamics, are found to be asymmetrical due to the specific shape of the driving voltage waveform. Tailoring the voltage waveform is shown to enable to control the electron energy probability function (EEPF) in distinct spatio-temporal regions of interest. As a consequence, the generation of reactive neutral species can be enhanced by increasing the number of consecutive harmonics. Based on a simplified two dimensional neutral transport model in the hybrid code, it is demonstrated that the transport between the electrodes, as well as the gas flow have different effects on various neutral species distributions due to the relevant chemical reaction rates for the generation and destruction of species.