We study scalar dark matter production and reheating via renormalizable inflaton couplings, which include both quartic and trilinear interactions. These processes often depend crucially on collective effects such as resonances, backreaction and rescattering of the produced particles. To take them into account, we perform lattice simulations and map out parameter space producing the correct (non-thermal) dark matter density. We find that the inflaton-dark matter system can reach a quasi-equilibrium state during preheating already at very small couplings, in which case the dark matter abundance becomes independent of the inflaton-dark matter coupling and is described by a universal formula. Dark matter is readily overproduced and even tiny values of the direct inflaton couplings can be sufficient to get the right composition of the Universe, which reaffirms their importance in cosmology.