If you are using another program while referring to the webpage & sticky note too, then you must stick the same sticky note to this "another program" also.
To learn more about this feature, watch this quick video:
To make the sticky note appear any time the web page is on the screen rather than only when it is has focus is technically not possible/feasible.
Since the sticky note is associated with the web page and not the monitor, the note will be visible as long as the web page is active. The moment you focus on any other app (doesn't matter which monitor), the sticky note disappears because you are no longer working on that web page.