The MATB-II is a computer display task, which aims to measure human control operations on a flight console. Using the MATB-II and a visual-search task measure of spatial attention, we tested if capture of spatial attention in a bottom-up or top-down way predicted performance in the MATB-II. This is important to understand for questions such as how to implement warning signals on visual displays in human–computer interaction. To measure visuospatial attention, we used both classical task-performance measures (i.e., reaction times and accuracy) as well as novel unobtrusive real-time pupillometry. A large number of analyses showed that: (1) Top-down attention measured before and after the MATB-II was positively correlated. (2) Test-retest reliability was also given for bottom-up attention, but to a smaller degree. As expected, the two spatial attention measures were also negatively correlated with one another. However, (3) neither of the visuospatial attention measures was significantly correlated with overall MATB-II performance, nor with (4) any of the MATB-II subtask performance measures. (5) Neither did pupillometry predict MATB-II performance, nor performance in any of the MATB-II’s subtasks. Yet, (6) pupil size discriminated between different stages of subtask performance in system monitoring. This finding indicated that temporal segregation of pupil size measures is necessary for their correct interpretation, and that caution is advised regarding average pupil-size measures of task demands across tasks and time points within tasks. Finally, we observed surprising effects of workload (or cognitive load) manipulation on MATB-II performance itself, namely, better performance under high- rather than low-workload conditions.