If you reply on an invitation email and accept oder decline a email to the event owner will be generated. When you accept oder decline in calendar event (not in email) no email will be send and event creator will not be informed.
We use Icewarp 12.1.1.4 as Groupware Server
Not all configurations will generate an email in eM Client to update your status. For example, using a CalDAV account in eM Client, the updates are handled by the calendar server not your desktop email client. That means you will not find the message in your Sent folder. However, the organizer will receive an email generated by the server confirming your status.
Maybe your server is not sending the notification.
If you have a Pro License, which I assume you do and are using the Icewarp re-branded version of eM Client, maybe open a support ticket with eM Client. If they are able to solve the problem, it would be interesting to hear how that happened.