How to trigger a Rules action based on which content pane of a panel is used?
Have a look at the Rules panes module. Some details about it (from its project page):

Rules Panes allow embedding Rules components as content panes in Panels (or so).
By default any parameters for the component are entered manually by the end user, but they can also be pre-populated with CTools contexts on the page (which will also hide the form input).

So if you can find a way to transform your &quot;... rules to perform some action ...&quot; in a Rules component, you should be good to go.
Some pointers to some more docu/demos about it (also mentioned on its project page):

Videos introducing this module.
Presentation from DrupalCamp Stockholm 2013.
Video about Rules panes.