The XML date format is:
yyyy-MM-dd
So, that is what your date picker is storing. You can change the format on the field that displays the date, if the field is a date data type. The data will be stored as 2013-01-12, but you can set the control to display 1/12/2013 - does that make sense? You can either look at a saved XML file in a text editor to see this, or add a calc'd value bound to the field and formatted to show the XML value to help you see what is going on.
Separating data from presentation is something InfoPath is very good at, but it can make things like this confusing.