The way it should work is that when the page loads the quote is returned and stored in your session variable. Then when it gets down to the shipping charges section it will retrieve the shipping quote values by executing the shipping rules. The values that are returned should show up as the shipping charges.
If you can post back with a copy of your WA_eCart folder in a zip archive I can take a look at the charge rule and do a test of it to see if I can get the charge to show. This will help to determine if the rule is the problem, the value it is working with or something else.