I think what you are missing is the dynamic adsorption equilibrium underlying the chromatography.
In general and in every chromatography, stationary phase is the one that is not moving, mobile phase is the one that is in motion - be it liquid or gas.
And every chromotography works exactly in the same way - solutes adsorb and desorb all the time (this is the dynamic equilibrium). When adsorbed on the stationary phase, solute stays in place. When desorbed - it moves together with mobile phase. The more time solute spends as adsorbed, the slower it move, the less time it spends as adsorbed, the faster it move.
Technical details will vary depending on the chromatography type, but general model is always the same.