A gold-capped Janus particle suspended in a near-critical binary liquid mixture can self-propel under illumination. We have immobilized such a particle in a narrow channel and studied the nonequilibrium dynamics of a binary solvent around it, using experiment and numerical simulations. For the latter we consider both a purely diffusive and a hydrodynamic model. All approaches indicate that the early time dynamics is purely diffusive and characterized by composition layers traveling with a constant speed from the surface of the colloid into the bulk. Subsequently, hydrodynamic effects set in and the transient state is destroyed by strong nonequilibrium concentration fluctuations, which arise as a result of the temperature gradient and the vicinity of the critical point of the binary liquid mixture. They give rise to a complex, permanently changing coarsening patterns. For a mobile particle, the transient dynamics results in propulsion in the direction opposite to that observed after the steady state is attained.