In digital control rooms, operators often need to monitor multiple information sources, which are spatially distributed on multiple screens, to manage multiple tasks simultaneously. Operators’ attention allocation between tasks are likely to be affected by the visual salience and eccentricity of secondary task screens. Their exact impacts and underlying mechanisms need to be investigated to inform system design to support balanced attention allocation strategies for optimal multitasking performance. This study aims to address these issues through a laboratory experiment using a simulated unmanned aerial vehicle monitoring platform. The participants performed a primary task and two secondary tasks concurrently, each shown on a separated screen. The visual salience and eccentricity of the maintenance task (one of the secondary tasks) were manipulated within-groups. Attention allocation behaviors were captured by eye movement data, and performance of both primary and secondary tasks were recorded. The participants were more likely to switch to and spent more time on the maintenance task of lower salience, showing a tendency to override the bottom-up influence of secondary task salience with top-down control. Large eccentricity of the secondary task, however, led to less attention allocation and lower task prioritization in paired event conflicts. The interaction effect of the salience and eccentricity of the maintenance task was significant for the accuracy of the primary task and the other secondary task. These findings offered insights into the joint design of salience and eccentricity of secondary tasks to enhance overall multitasking performance.