Cognitive control has been investigated in attentional conflict tasks for a long time. One representative phenomenon of adaptive cognitive control in these tasks is the congruency sequence effect (CSE), which means that a previous conflict will lead to reduced congruency effects at the current moment, reflecting increased control of attention toward the task at hand. One debating question is whether CSE can generalize between different conditions. Since a similar phenomenon (i.e., validity sequence effect, VSE) has been found in spatial cueing tasks, this study investigated whether the two sequential effects could generalize between each other. A cross-task sequence effect is found from previous flanker trials to current cueing trials when the task sets of the two tasks are either very similar or sufficiently dissimilar, and this C-VSE effect is influenced by the response mode of the experimental design. In addition, the VSE between trial n-2 and trial n is eliminated by the existence of an intermediate flanker trial, but the CSE between trial n-2 and trial n is still significant even with an intermediate cueing trial. Possible explanations of these findings are discussed. The findings suggest a close connection between orienting and executive control processes in attention networks and provide a new perspective and method for investigating the potential mechanisms of cognitive control.