We derive the cross section for the diffractive gluon production in high energy onium-nucleus collisions that includes the low-x evolution effects in the rapidity interval between the onium and the produced gluon and in the rapidity interval between the gluon and the target nucleus. We analyze our result in two limiting cases: when the onium size is much smaller than the saturation scale and when its size is much larger than the saturation scale. In the later case the gluon multiplicity is very small in the quasiclassical case and increases when the low-x evolution effects in onium become significant. We discuss the implications of our result for the Relativistic Heavy Ion Collider, Large Hadron Collider, and Electron Ion Collider phenomenology.