There's also the browser cache, and possibly a cache system on the server. I don't believe that the results of $modx->runSnippet() are ever cached, but I could be wrong.
I assume that you're calling the snippet uncached. You can try making the page itself uncached to see if that has an effect.
You can look at the raw cache files in the core/cache directory to see what MODX is, and isn't, caching. Make a note of the snippets' IDs first.
You can cache-bust the file to keep the browser from caching it by adding a fake param on the end of the URL:
$url .= '?param=hello&id=' . time();
You can also do something like this in a plugin:
header('Cache-Control: no-cache, no-store, must-revalidate'); // HTTP 1.1.
header('Pragma: no-cache'); // HTTP 1.0.
header('Expires: 0'); // Proxies.
I'm not sure what the correct event would be -- maybe OnWebPagePrerender.