You can connect it to the 2nd battery if you like and it will get charged. However, I feel the proper way to do it since you have a dual battery controller (you still haven't said what kind and YES this may make a difference) I would plug the panel into your main battery. On a National Luna setup or IBS you will eventually hear the soloenoid click. This then allows the charge from the panel to flow from the main battery which is now sufficiently charged to your 2nd battery.
Sorry, I'm using a Dirty Parts kit with a yellow top second battery. Thanks again for the help.