Adapting attention flexibly is a fundamental ability of the human control system. A primary example of this ability is demonstrated by the fact that, in the color-word Stroop task, congruency effects are typically smaller for colors and words that mainly appear in incongruent stimuli (mostly-incongruent items) than for colors and words that mainly appear in congruent stimuli (mostly-congruent items). Recent research suggests that at least part of this item-specific proportion-congruent (ISPC) effect is due to a process of reactive conflict adaptation that affords higher selectivity (i.e., more efficient selection of task-relevant information) when mostly-incongruent items are presented. However, what stimulus component (task-relevant, task-irrelevant, or both) triggers this conflict-adaptation process is currently unclear. While it was earlier conjectured that this process would be based on the task-irrelevant component, more recent research suggested that the task-relevant component could be the trigger (e.g., recognizing a mostly-incongruent color, rather than a mostly-incongruent word, would induce higher selectivity), but only if the ISPC paradigm is modified to favor use of that trigger. Using a color-word and a spatial Stroop task in which use of neither trigger was favored but it was possible to dissociate task-relevant and task-irrelevant triggering processes, we found evidence for both processes, with the two triggers having approximately equivalent impacts. These results challenge views of the ISPC effect according to which, in general, the ISPC effect involves conflict-adaptation processes only in special situations. The ISPC may involve conflict-adaptation processes in most situations, with both task-relevant and task-irrelevant information triggering such processes.