We use NIRCam imaging from the JWST Advanced Deep Extragalactic Survey (JADES) to study the ionising properties of a sample of 14652 galaxies at 3 ≤ zphot ≤ 9, 90% complete in stellar mass down to log(M⋆/[M⊙]) ≈ 7.5. Out of the full sample, 1620 of the galaxies have spectroscopic redshift measurements from the literature. We use the spectral energy distribution fitting code Prospector to fit all available photometry and infer galaxy properties. We find a significantly milder evolution of the ionising photon production efficiency (ξion) with redshift and UV magnitude than previously reported. Interestingly, we observe two distinct populations in ξion, distinguished by their burstiness (given by SFR10/SFR100). Both populations show the same evolution with z and MUV, but have a different ξion normalisation. We convolve the more representative log (ξion(z, MUV)) relations (accounting for ∼97% of the sample), with luminosity functions from literature, to place constraints on the cosmic ionising photon budget. By combining our results, we find that one of our models can match the observational constraints from the Lyα forest at z ≲ 6. We conclude that galaxies with MUV between −16 and −20, adopting a reasonable escape fraction, can produce enough ionising photons to ionise the Universe, without exceeding the required ionising photon budget.