The order of the triggers does not matter for spot processing – all triggers are always checked; it’s not a “first match wins” ruleset type of thing. If multiple triggers match a given spot, then all of the (joint) actions will be performed. If you have comments set on your triggers, then the HamAlert app will show the ones that matched in the spot details, and the comma separated trigger comments are also available in the triggerComment field of the URL POST.
I’m not sure what went wrong in your case. To be sure, I just gave it a try by defining two triggers, one with a callsign condition and a URL action, and another one with a park reference condition and an App action. Simulating a spot for that callsign and park reference (in the comments field of the Simulate screen) triggered both actions.
BTW, for the visual overview, you can influence trigger sorting in the web interface by leveraging the fact that they are sorted alphabetically by trigger comment: