Looking at the code you have on these checkout pages it seems that either approach should work, but you will need to have this code on your confirm page, not the checkout. This is because the form on the checkout page posts to the confirm page, so the triggers you are using are valid when placed on the confirm page.
You should open your confirm page and add in the DataAssist Insert server behavior here. You may want to update the trigger though to work the button on this page.