The extension is not choosing the wrong type, you are. when setting up the column bindings, you need to select the data type. The extension may preselect the integer data type since that is the data type in the database, but it has know way of knowing that the field feeding the data is a checkbox. in the case where you are using a checkbox, you need select to use the checkbox data type.
It shouldn't be working on the update page if you don't select to use the checkbox data type, so i really cant explain why it works there, but the long and short, regardless, is that you should be selecting the checkbox 1/0 data type in the insert and in the update behaviors when using a checkbox as the form element.