Theoretical models suggest that maintenance and updating are two functional states of working memory (WM), which are controlled by a gate between perceptual information and WM representations. Opening the gate enables updating WM with input, while closing it enables keeping the maintained information shielded from interference. However, it is still unclear when gate opening takes place, and what is the external signal that triggers it. A version of the AX-CPT paradigm was used to examine a recent proposal in the literature, suggesting that updating is triggered whenever the maintenance of the context is necessary for task performance (context-dependent tasks). In four experiments using this paradigm, we show that (1) a task-switching cost takes place in both context-dependent and context-independent trials; (2) task-switching is additive to the dependency effect, and (3) unlike switching cost, the dependency effect is not affected by preparation and, therefore, does not reflect context-updating. We suggest that WM updating is likely to be triggered by a simple mechanism that occurs in each trial of the task regardless of whether maintaining the context is needed or not. The implications for WM updating and its relationship to task-switching are discussed.