We present an analysis of the diffuse ionised gas (DIG) in a high-resolutionsimulation of an isolated Milky Way-like galaxy, incorporating on-the-flyradiative transfer and non-equilibrium thermochemistry. We utilise theMonte-Carlo radiative transfer code COLT to self-consistently obtain ionisationstates and line emission in post-processing. We find a clear bimodaldistribution in the electron densities of ionised gas ($n_{\rm e}$), allowingus to define a threshold of $n_{\rm e}=10\,\mathrm{cm}^{-3}$ to differentiateDIG from HII regions. The DIG is primarily ionised by stars aged 5-25 Myr,which become exposed directly to low-density gas after HII regions have beencleared. Leakage from recently formed stars ($<5$ Myr) is only moderatelyimportant for DIG ionisation. We forward model local observations and validateour simulated DIG against observed line ratios in [SII]/H$\alpha$,[NII]/H$\alpha$, [OI]/H$\alpha$, and [OIII]/H$\beta$ against $\Sigma_{\rmH\alpha}$. The mock observations not only reproduce observed correlations, butalso demonstrate that such trends are related to an increasing temperature andhardening ionising radiation field with decreasing $n_{\rm e}$. The hardeningof radiation within the DIG is caused by the gradual transition of the dominantionising source with decreasing $n_{\rm e}$ from 0 Myr to 25 Myr stars, whichhave progressively harder intrinsic ionising spectra primarily due to theextended Wolf-Rayet phase caused by binary interactions. Consequently, the DIGline ratio trends can be attributed to ongoing star formation, rather thansecondary ionisation sources, and therefore present a potent test for stellarfeedback and stellar population models.