You can use Zapier's filters to customize notification rules for specific types of issues. For instance, you may want to receive an SMS if there are ever any new issues in the "Security" category for your project, or maybe when there is a new issue with a status of "Critical".
Alternatively if your team is separated into designers and developers who each have their own group chat room in a messaging app that integrates with Zapier, like Slack or Campfire, you can route all issues in the "Design" project or with the category "Design" to the design chatroom. Alternatively, you could route "Critical" issues in the "Security" category to the developer chatroom.
Being able to select which new issues trigger Zaps based on project, status, etc. and having so many potential target apps and actions provides endless possibilities to keep your team notified.
Here's a list of all the potential filters, along with Project, for new issues. The grey text on the right is just an example of the data the field would contain. You can use any of these attributes to adjust which notifications are routed to which application.