Hi,
That access log is quite interesting.
The first log is a request from your payment gateway to the notification URL of your plugin:
194.74.4.166 - - [06/Jul/2016:14:36:01 +0100] "POST /index.php?option=com_hikashop&view=checkout&layout=notify¬if_payment=securetradingppages HTTP/1.1" 200 403 "-" "SecureTrading STPP Gateway"
That's the request you had to look for.
As it gives a 200 HTTP return code, it means that the request is successful, and thus if the payment plugin is properly coded, with the debug option activated it should add debug data in the payment log of the HikaShop configuration.
If the payment log is empty even though you have that log and the debug option is activated, there is a problem with the payment plugin code.
The second log is the redirection of the customer from the payment page to the website which also goes through the paymnet notification but only to redirect the customer to the after_end view (the thank you page). So that why you get a 302 redirect HTTP return code. So that's functioning properly.