We examine the impact of black hole jet feedback on the properties of the low-redshift intergalactic medium (IGM) in the SIMBA simulation, with a focus on the Ly$alpha$ forest mean flux decrement $D_A$. Without jet feedback, we confirm the Photon Underproduction Crisis (PUC) in which $Gamma_{rm HI}$ at $z=0$ must be increased by $times6$ over the Haardt & Madau value in order to match the observed $D_{A}$. Turning on jet feedback lowers this discrepancy to $simtimes 2.5$, and additionally using the recent Faucher-Gigu`ere background mostly resolves the PUC, along with producing a flux probability distribution function in accord with observations. The PUC becomes apparent at late epochs ($z lesssim 1$) where the jet and no-jet simulations diverge; at higher redshifts SIMBA reproduces the observed $D_{A}$ with no adjustment, with or without jets. The main impact of jet feedback is to lower the cosmic baryon fraction in the diffuse IGM from 39% to 16% at $z=0$, while increasing the warm-hot intergalactic medium (WHIM) baryon fraction from 30% to 70%; the lowering of the diffuse IGM content directly translates into a lowering of $D_{A}$ by a similar factor. Comparing to the older MUFASA simulation that employs different quenching feedback but is otherwise similar to SIMBA, MUFASA matches $D_{A}$ less well than SIMBA, suggesting that low-redshift measurements of $D_{A}$ and $Gamma_{rm HI}$ could provide constraints on feedback mechanisms. Our results suggest that widespread IGM heating at late times is a plausible solution to the PUC, and that SIMBAs jet AGN feedback model, included to quench massive galaxies, approximately yields this required heating.
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