Radiation pressure can be dynamically important in star-forming environments such as ultra-luminous infrared and submillimetre galaxies. Whether and how radiation drives turbulence and bulk outflows in star formation sites is still unclear. The uncertainty in part reflects the limitations of direct numerical schemes that are currently used to simulate radiation transfer and radiation–gas coupling. An idealized setup in which radiation is introduced at the base of a dusty atmosphere in a gravitational field has recently become the standard test for radiation-hydrodynamics methods in the context of star formation. To a series of treatments featuring the flux-limited diffusion approximation as well as a short-characteristics tracing and M1 closure for the variable Eddington tensor approximation, we here add another treatment that is based on the implicit Monte Carlo radiation transfer scheme. Consistent with all previous treatments, the atmosphere undergoes Rayleigh–Taylor instability and readjusts to a near-Eddington-limited state. We detect late-time net acceleration in which the turbulent velocity dispersion matches that reported previously with the short-characteristics-based radiation transport closure, the most accurate of the three preceding treatments. Our technical result demonstrates the importance of accurate radiation transfer in simulations of radiative feedback.