Computational models of decision making are becoming increasingly popular to interpret reaction time and choice data in terms of decision and non-decision related processes. But current evidence remains scarce as to whether parameters of a mathematical model such as the Drift Diffusion Model (DDM) can recover genuine latent psychological processes. In this study, we combine an experimental approach using a decision making task with a physiological decomposition of each reaction time into a motor and pre-motor time using electro-myography. The aim is to test whether the non-decision time parameter of a DDM, assumed to contain encoding and motor processes, varies according to both psychophysical predictions of stimulus encoding and the physiological measurement of motor processes. Our results show that 1) the encoding time is accounted by a DDM only in the case of instructions emphasizing speed over accuracy and 2) that the onset of muscular activity does not sign the end of the accumulation of evidence. This questions the ability of DDM to account for how participants achieve speed-accuracy tradeoff as well as the interpretability of its parameters in terms of decision and non-decision processes.