When you opened your Schema to edit it, you got a notification indicating that your changes would not be updated in derived Components.
(in 2013 SP1 it mentions Changes to this Schema will affect all related items. together with a Show Where Used button, agreed this isn't as clear as it was stated in older versions, but I believe this is the least read message anyways, so no matter what it said, people just don't seem to be willing to read it).
Also the documentation you mentioned specified this with the following note:
Note: Existing items based on the Schema are not automatically
updated. For example, if you remove a field from a Component Schema,
Components based on that Schema that have a value set for the removed
field will continue to contain that value. The value will only be
removed when the Component is opened and saved, either in the Content
Manager Explorer GUI or when using the Content Porter application.
To update all derived Components, you have to (manually) edit all those Components. On some changes, the UI will already try to fix your changes (like removing values for fields which are no longer in the Schema, or reordering fields according to the Schema), but I don't think a field rename is something that the UI can cater for (apart from the order there is no way of identifying which field you renamed).
So options you have are:
- Manually open all Components and fix the content.
- List item Write a (Core Service) script which will change the content of all affected Components
Last thing, which is not a real option perhaps, don't make the change, just change the description of the field in the Schema and leave the XML name as is.