Important: If you are a Zammad Support or hosted customer and experience a technical issue, please refer to: support@zammad.com using your zammad-hostname / or company contract.
Used Zammad version:
Used Zammad installation source: (source, package, …)
Standard notifications (ticket created, ticket assigend, ticket updated) should be sent to the agent without any trigger if your email settings are correct.
Anything in addition to that should be done with triggers, yes.
Like @MrGeneration said check in the agent profile that the email notification is set enabled, also when setting up Zammad first time you set up a smtp server, thus is what is being used im sure to email agents not the email groups that the customer come in on and get replies on
hope that helps