When no one modify the date in the picker, then defaultDate has to be used.
The problem is that this defaultDate is stored without converting it into the submitFormat that I have choose.
$("#date").dateDropdowns({
submitFieldName: 'date',
submitFormat: 'mm/dd/yyyy',
defaultDate: '2001-02-01'
});
In this case, if I submit the value this will remain 2001-02-01 and never been changed to the submitFormat requested.