Your store cart details server behavior is triggered on any page post. This checkout page does not post to itself so the trigger is not occurring.
If you want to store this info in the db when the user gets to the checkout page you should update the trigger to be before page load. The store order summary server behavior will insert a record for each item that is in the cart. If you want to insert a single record for the entire order you would wan to use the store order summary server behavior.
This will get the record in your db, but you can't rely on the presence of this record to confirm that the payment has been made. The only way you can do that with a remote checkout like Payments Standard is to have the insert occur on the IPN page after you check for a successful transaction.