All Kartris payment systems, if configured appropriately, should send confirmation emails from your site to both the store owner and the customer. If this does not happen, there are normally two possible reasons.
1. Callback not configured properly
On most payment systems, the customer is redirected to a secure page on the gateway's own secure server. When they complete payment here, the gateway's server calls the Callback.aspx page on your site to notify it. Kartris can then check the appropriate status boxes for the order and send its confirmation emails. Please read the setup instructions within the Kartris User & Developer Guide for the particular payment system you're using and ensure that everything is correct, especially the setup within the gateway's own admin panel.
A quick way to confirm if bad callback configuration is to blame is to look into the recent orders on your back end. If the orders made show up under recent orders, and show a comment in the status box such as 'Your order was passed by the online payment gateway at 01/04/2014 11:45:02', then the callback is configured correctly and working. If the orders don't show up, then you should generally be able to see them in the 'unfinished' queue. This indicates that the callback either did not occur, or failed for some reason.
Kartris will log all hits on the Callback.aspx page in the error logs (these aren't errors, but are still useful to have logged). If callbacks are failing, you should be able to check the logs to see if any reason is recorded - search for 'callback' and you should find any records. If you don't find any record of callbacks, this suggests that the callback is not even hitting Kartris, so check your gateway admin panel and ensure the notification/callback URL is correct and callbacks are turned on.
2. Email server or mail settings not configured properly
If your callbacks are working (orders show up in the 'recent orders' rather than 'unfinished' in the back end of Kartris) but you're still not receiving emails, then the issue is most likely with your email setup. In the Kartris config settings, search for 'mail' and the system will find several config settings for configuring email. On shared hosting, you will need to confirm with your host the correct values to use for these settings. You can easily test email by doing a password request, or by using the contact form. Try varying the email addresses used, for example if the contact form does not seem to reach your company email, try changing the contact email address to a hotmail or gmail account.
If you are running your own server, ensure that the SMTP service is running and properly configured. Doing this is beyond the scope of our support, but there are many resources on the web regarding this. Sometimes, you will find that the email addresses used either as the FROM or TO fields affect whether mail is sent. You may also find issues with spam filters blocking mail; SPF records in your DNS and configuring rDNS on the server will typically be required to maximize the reliability of delivery. Your server provider should be able to help with these if you are having problems.
If email is not working and you believe your settings are correct, it's important that you verify this by using a simple test script. If you cannot get a test script sending mail correctly, then the issue is clearly outside of Kartris. If your test script can send email and Kartris cannot, ensure that the settings match - in particular, the email addresses used. Quite often bad server configuration can mean that a particular site will happily send email from or to particular addresses, while not to others.