I am using Bootstrap 3 DateTimePicker and I am trying example 8 (Linked datetimepicker).
This may seem silly, but did you check you're using the same bootstrap-datetimepicker.js plugin that you're referring to in your question?
There are two versions I know of which are very similar:
The first version responds to change.dp, while the second version responds to dp.change.
Just check the comments at the top of the bootstrap-datetimepicker.js to see which one you're using.