You're pretty close.
By Triggering Agent: user roles that have visibility of the device will be able to see the alert generated
Example:
UserA and UserB have different roles (RoleA, RoleB) restricting visibility of BuildingA and BuildingB respectively. AMP admin creates trigger with visibility by triggering agent. AP in BuildingA causes trigger to fire -> only UserA can see the alert, UserB does not see the alert. Admin users would have visibility of all.
By Role: user roles that match the role of the user who created the alert will have visibility of alerts generated
Example:
UserA creates a trigger, it fires. UserB does not have visibility since their role is not the same.
Admin creates a trigger -> only other Admin users can view.