For the Original: 
Yes, it can be used with past covers. However, please note that the design of the Cover on Cover was updated in 2013, so it may not fit perfectly on covers from 2012 or earlier. 

For the Cousin: 
It is compatible with covers from 2014 and later. Due to a size change in 2014, it cannot be used with Cousin covers from 2013 or earlier.