Studies on the intuitive or deliberate nature of human actions often use time constraints for identification, assuming that constrained individuals fall back to intuitive behavior. This identification strategy disregards individual heterogeneity and self-priming, i.e. the behavioral rule that subjects can form during the instructions phase, and then apply irrespective of the time constraint. We use respondent data from an impunity game as an example of how subject heterogeneity can drive results. 24 respondents face 240 more or less unfair allocation proposals out of a small or large pie and can accept or reject the offer. Upon rejection respondents burn their own money, but not the proposer's. Respondents decisions are communicated to the proposer. On average, emotional rejections take longer than deliberate acceptances. Including individual heterogeneity, though, we find that subjects who mostly accept (reject) take more time to reject (accept). Faster decisions are the ones conforming with the modal early reaction. We attribute this finding to heterogeneity in self-priming. Since self-priming is orthogonal to time constraints, it has the capacity to invalidate their use in the identification of dual decision modes.