The APSIS reactor has been designed to simulate in the laboratory with a VUV synchrotron irradiation the photochemistry occurring in planetary upper atmospheres. A N₂-CH₄ Titan-like gas mixture has been studied, whose photochemistry in Titan's ionospheric irradiation conditions leads to a coupled chemical network involving both radicals and ions. In the present work, an ion-neutral coupled model is developed to interpret the experimental data, taking into account the uncertainties on the kinetic parameters by Monte Carlo sampling. The model predicts species concentrations in agreement with mass spectrometry measurements of the methane consumption and product blocks intensities. Ion chemistry and in particular dissociative recombination are found to be very important through sensitivity analysis. The model is also applied to complementary environmental conditions, corresponding to Titan's ionospheric average conditions and to another existing synchrotron setup. An innovative study of the correlations between species concentrations identifies two main competitive families, leading respectively to saturated and unsaturated species. We find that the unsaturated growth family, driven by C₂H₂ , is dominant in Titan's upper atmosphere, as observed by the Cassini INMS. But the saturated species are substantially more intense in the measurements of the two synchrotron experimental setups, and likely originate from catalysis by metallic walls of the reactors.