We use the Auriga simulations to probe different satellite quenching mechanisms operating at different mass scales ($10^5 \, \mathrm{M}_\odot \lesssim M_\star \lesssim 10^{11} \, \mathrm{M}_\odot$) in Milky Way-like hosts. Our goal is to understand the origin of the satellite colour distribution and star-forming properties in both observations and simulations. We find that the satellite populations in the Auriga simulations, which was originally designed to model Milky Way-like host galaxies, resemble the populations in the Exploration of Local VolumE Satellites (ELVES) Survey and the Satellites Around Galactic Analogs (SAGA) survey in their luminosity function in the luminosity range -12 ≲ MV ≲ -15 and resemble ELVES in their quenched fraction and colour-magnitude distribution in the luminosity range -12 ≲ Mg ≲ -15. We find that satellites transition from blue colours to red colours at the luminosity range -15 ≲ Mg ≲ -12 in both the simulations and observations and we show that this shift is driven by environmental effects in the simulations. We demonstrate also that the colour distribution in both simulations and observations can be decomposed into two statistically distinct populations based on their morphological type or star-forming status that are statistically distinct. In the simulations, these two populations also have statistically distinct infall time distributions. The comparison presented here seems to indicate that this tension is resolved by the improved target selection of ELVES, but there are still tensions in understanding the colours of faint galaxies, of which ELVES appears to have a significant population of faint blue satellites not recovered in Auriga.