Symptoms

dd/MM/yyyy switches to MM/dd/yyyy after pasting the value to the Calendar control
 

Diagnoses

The behaviour is as expected since it parses the value based on the selected region's format prior to applying the styling set (dd/MM/yyyy):

1. Read input value using the regional format set -andgt English (United States) = MM/dd/yyyy
eg. 08/04/2016

2. Apply the styling (dd/MM/yyyy)
eg. 04/08/2016
 

Resolution

Change the Language/Region in your Custom Style Builder to a region which uses the same format.