In theory, it should work...
That said, maybe there are conditions that are preventing the rules from firing, or perhaps a JS error that is failing something before the rule can properly complete.....
As for creating a new Property Tag... I usually play that by ear... depending on the complexity of my tracking, and how significantly different the site code is, etc.... For instance, we have about 30 websites using the same base code, so I use 1 property for all the sites (using Data Elements and logic to set the cookies first party for each site, and to swap out the tracking server to again be first party, etc).... however, each of those sites have "extended content" on sub-domains, and those have a very different code base, so I have a separate property for each sub-domain variant (where the tracking goes to the same suite, sets the data to the same dimensions and using the same naming conventions, etc), but I can optimize the tracking to the code base.
Do you see any JS errors in your browser's console? Also, have you tried enabling the Satellite Debugger to see what might be happening?
// Turn on debugging
_satellite.setDebug(true);
// Turn off debugging
_satellite.setDebug(false);
Hopefully this can help you find something about what is happening, and if you are willing to share a link (even via private messaging) I would be happy to take a look and see if I can find anything.
