Geometrical constraints, specifically the alignment of relativistic jet with the observer’s line of sight, make blazars the rarest and most powerful active galactic nuclei. They show extreme variability on different time-scales depending on the wavelength. Flares last from typical sub/few- hours in X-rays and TeVs, to months or years in the radio. Based on this observational evidence of radio-gamma delays with timescales ranging from weeks to months, we build, using the JetSeT framework, a self-consistent model of a relativistic expanding jet, taking into account all the radiative and accelerative processes acting in blazar jets. We present phenomenological predictions, validated by the numerical models, using a radio-gamma response profile including the delay, rising and decaying timescales, constraining expansion velocity and properties of the blob environment. We compare these predictions to results from temporal analysis of the BL Lacs object Mrk 421, finding a satisfactory agreement between the phenomenological trends and observations, and we derive constraints on the structure of the magnetic field and the location of the blazar zone.