Slow Statues Change Due To Smtp

I'm currently using zoho mail server to send out all the emails from the cart in order to avoid going to the spam folder. However I notice when there is a new order or i change the order statues, the emailing process takes 10 to 12 secs.

I have reached out to zoho helpdesk and they are now asking for

"Please share the time stamp and the connecting logs between your Shopping cart and our SMTP server along with the originating IP address for further analysis."

I tried going to the log in the admin, but couldn't find anything involving emails.

Can anyone tell me where to find the connection log? or have any suggestion to spend up the emailing process.