As far as I can see David Couper Smith's estate passed to widow, Louise in 1904. In the 1911 Census at 95 South Street, St Andrews we have
Louise Smith, Head, widow, 70, Housekeeper
Alex.C. Smith, Son, single, 34, Lithographic artist Printing Works, worker
Albert D. Smith, Son, single, Watchmaker& jeweller, employee
It may be that the business carried on as "David Smith" but judging by the appearance of the clock 1904 would be well after its manufacture.
In the top illustration (maybe Flora MacDonald) is there a signature bottom right? Maybe the name of the dial painter. Maker of the dial may be stamped on back of dial. If so this might give another identifier to date the clock.
Dod