Task batteries mimicking user tasks are of high heuristic value. Supposedly, they measure individual human aptitude regarding the task in question. However, less is often known about the underlying mechanisms or functions that account for task performance in such complex batteries. This is also true of the Multi-Attribute Task Battery (MATB-II). The MATB-II is a computer display task. It 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 and for what to practice during training of operating with such displays. 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. The latter was done as pupil size covaries with task demands. 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. The latter was true even if the subtask required visuospatial attention (as in the system monitoring task of the MATB-II). (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. The latter findings imply that the MATB-II itself poses a number of questions about its underlying rationale, besides allowing occasional usage in more applied research.