Currently if you try to add an item to a reading list using the Add item/My collection option in the right-hand pane, there is no refresh option (unlike in My Collection proper which does have at least a refresh button. If users add items using cite it or push to my Collection from Primo, the list is not updated automatically and so it appears that the My Collection is not correctly updating.
Adding a refresh would ensure the option shows all added resources as soon as they are available.