Two-choice reaction tasks for which stimuli differ on irrelevant and relevant dimensions (e.g., Simon, flanker, and Stroop tasks) show congruency effects. The diffusion model for conflict tasks (DMC) has provided a quantitative account of the mechanisms underlying decisions in such conflict tasks, but it has not been applied to the congruency sequence effect (CSE) for which the congruency on the prior trial influences performance on the current trial. The present study expands analysis of the reaction time (RT) distributions reflected by delta plots to the CSE, and then extends the DMC to simulate the results. With increasing RT: (1) the spatial Simon effect was almost unchanged following congruent trials but initially became smaller and finally reversed following incongruent trials; (2) the arrow-based Simon effects increased following both congruent and incongruent trials, but more so for the former than the latter; (3) the flanker congruency effect varied quadratically following congruent trials but increased linearly following incongruent trials. These results were modeled by the CSE-DMC, extended from the DMC with two additional assumptions: (1) feature integration influences only the controlled processes; (2) following incongruent trials, the automatic process is weakened. The results fit better with the CSE-DMC than with two variants that separately had only one of the two additional assumptions. These findings indicate that the CSEs for different conflict tasks have disparate RT distributions and that these disparities are likely due to the controlled and automatic processes being influenced differently for each trial sequence.