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 T c and the temperature T crit , 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 T crit . At temperatures above T crit , 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'.