In Modern UX in the Cross-Project Task list the user will see ALL tasks with the Project - View Tasks - All access right on this page.
CA PPM APPLICATION
In Modern UX if you want users to use the Cross-Project Task list and not see ALL tasks, then do not use the GLOBAL rights for Task View or Task Management. The one page was designed to show all tasks with the global rights in modern UX, however in Classic it does not.
Please see Clarity documentation here for more information.
Project - View Tasks - All
Allows users to view tasks and work breakdown structure for any project the user has been
Note: If you allocate this access rights to a user, they will see all the tasks for all projects in Clarity (formerly known as the New User Experience). If you want, users to access only tasks allocated to them, please use instance rights.