  We study the dynamics of a non-minimally coupled (NMC) scalar spectator field
in non-oscillatory inflationary scenarios, where there is a transition from
inflation to kination domination (KD). Engineering a realistic finite-duration
transition through a CMB-compatible inflaton potential, we calculate the
initial tachyonic growth of the NMC field during KD and perform lattice
simulations of the subsequent non-linear dynamics. We characterize the
regularization effect on the tachyonic growth, either due to self-interactions,
or via gravitational backreaction when the NMC field grows to dominate the
energy of the universe. Our study provides the first realistic treatment of the
dynamics, with significant improvements compared to previous work, where one or
more of the following aspects were assumed: ($i$) the background expansion can
be neglected during the tachyonic growth, ($ii$) coherence of the NMC field,
($iii$) coherence of the inflaton, ($iv$) instantaneous transition, and ($v$) a
KD equation of state of exactly $w = 1$. Using our methodology, which requires
none of the above assumptions, we determine the conditions to achieve proper
reheating, i.e. energetic dominance of the NMC field over the inflaton. We
characterize the time and energy scales of the problem, either for backreaction
due to self-interactions, or (as a novelty of this work) due to gravitational
effects. Finally, we calculate $\mathcal{O}(1)$ lattice correction factors to
analytic scaling relations derived by some of us in previous work. This enables
simple future studies without the need to run lattice simulations.
