There's enough evidence to suggest that this watch was not specifically issued for the Dominion Atlantic Railway. There were a few other railways that used the term Dominion in their names.
Most notably Great Falls and Old Dominion Railway, The Western Dominion Railway Company or The Washington and Old Dominion Railroad.
Alternatively, in Canadian law you will find the we had the Dominion Railway Act that could have been the source of the term Dominion Railways:
http://books.google.com.br/books?id=pYc ... ct&f=false
There is even a historical society called the Old Dominion Railway Historical Society out of Richmond Virginia. This might have also been the source of the term Dominion Railways at the time the watch was made.
Of further interest to you, I also found a thread from another message board that deals specifically with this watch that you might find interesting in regards to persuing the history of this watch. Apparently you are in rare company with this beautiful time piece even though many were made at that time.
I will continue to keep my eye out for any further information on this timepiece. I would be very pleased in fact to discover evidence that this was specifically a DAR watch!