Increasingly higher demands are being made on the capacity-limited cognitive capabilities of human operators as they strive to maintain situation awareness (i.e., understanding "what is going on") and performance in complex tasks. In the current study we asked whether: (a) training administered via a mobile phone-based app could improve multitasking and (b) improved multitasking in the app would generalize to improved performance and situation awareness in a simulated air traffic control task (ATC). Participants completed the ATC task before and after multiple sessions of app-based multitasking training or control training. Multitasking on the app improved across training sessions. However, this did not lead to improved performance or situation awareness, or workload reduction, relative to control training on the ATC task. These outcomes indicate that app-based multitasking training based on repetition of a single training task will not necessarily yield generalizable benefits to human performance in other complex dynamic tasks.