The extraplanar diffuse ionised gas (eDIG) is a key component for understanding the feedback processes that connect galactic discs and their halos. In this paper, we present the second study of the Bidimensional Exploration of the warm-Temperature Ionised Gas (BETIS) project, the aim of which is to explore the possible ionisation mechanisms and characteristics of the eDIG. We use a sample of eight edge-on galaxies observed with the Multi-Unit Spectroscopic Explorer (MUSE) integral field spectrograph (IFS) and apply the methodology developed in the first paper of the BETIS project for obtaining binned emission line maps. We find that the vertical and radial profiles of the [N II]/Hα, [S II]/Hα, [O III]/Hβ, and [O I]/Hα ratios depict a complex ionisation structure within galactic halos – which is influenced by the spatial distribution of H II regions across the galactic plane as observed from our line of sight–, with Lyman continuum photon leakage from OB associations constituting the main ionisation source. Moreover, the electron temperature and S+/S ionisation ratio also exhibit a dependency on the distribution of H II regions within the galactic discs. Our analysis excludes low-mass, hot, and evolved stars (HOLMES) as viable candidates for secondary ionisation sources to elucidate the unusual behaviour of the line ratios at greater distances from the galactic midplane. In contrast, we ascertain that shocks induced in the interstellar medium by star formation(SF)-related feedback mechanisms represent a promising secondary ionisation source of the eDIG. We present a suite of models integrating ionisation mechanisms arising from fast shocks and photoionisation associated with star formation. When applied to the classical Baldwin–Phillips–Terlevich (BPT) diagrams, these models reveal that the ionisation budget of the eDIG ranges from 20% to 50% across our sample, with local variations of up to 20% within individual galaxy halos. This contribution correlates with the presence of filaments and other structural components observed within galaxy halos. The presence of shocks is additionally supported by the observation of a high density of high [O I]/Hα ratios, which is characteristic of shock-compressed ionised gas, and is likely induced by feedback from regions of intense SF within the galactic disc. These results demonstrate consistency across all galaxies analysed in this sample.