Here, we study the temporal evolution of the magnetic field-driven paramagnetic to ferromagnetic transition in the La(Fe,Mn,Si)13 material family. Three compositions are chosen that show varying strengths of the first-order character of the transition, as determined by the relative magnitude of their magnetic hysteresis and temperature separation between the zero-field transition temperature Tc and the temperature Tcrit, where the transition becomes continuous. Systematic variations in the fixed field, isothermal rate of relaxation are observed as a function of temperature and as a function of the degree of first-order character. The relaxation rate is reduced in more weakly first-order compositions and is also reduced as the temperature is increased towards Tcrit At temperatures above Tcrit, the metastability of the transition vanishes along with its associated temporal dynamics.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'.