You need to add a new panel to the second screen, and add a task amangermanager to that.
Right-click on the background of the second screen -> Add Panel
-> Empty Panel
.
If you know how to move panels and add widgets to the panel, then move the panel to where you want it, add the tasks widgets, then set it to also only show widgets from the current screen.
If you don't know, then read on:
Right-click on the panel -> Panel Settings
then drag the Screen Edge
bar to the bottom of the screen to move the panel. Then right click on the panel -> Add Widgets
-> Double-click on Task Manager
. Then right-click somewhere near the middle of the panel -> Task Manager Settings
-> Only show tasks from the current screen