I think the problem lies in DMLOptions Email Header is not enabled while you are inserting your case comment in your trigger.
You should be doing something like this before calling insert operation on case comment instance
Database.DMLOptions opts = new Database.DMLOptions();
opts.EmailHeader.triggerAutoResponseEmail = true;
opts.EmailHeader.triggerOtherEmail = true;
opts.EmailHeader.triggerUserEmail = true;
After looking through comments, i googled and found this SFSE question which mentions this cannot be achieved. As a workaround,
- Insert case comments using your trigger.
- On insert of case comment, write a workflow to update a field (say a
check box called "send email notification" on the case).
- On the case, write a workflow email alert to notifying the contact
when the "send email notifcation" is updated.
Hope this helps.