They switched [1] as early as 1977 to Seiko after a brief flirt with Breitling, then to Omega from 1995 although Rolex did briefly reappear in 1989.
In other words much of today's target market did not see Bond wear a Rolex in cinemas, and it is a testimony to the strength of Rolex's brand that Omega's own product placement has been hijacked in people's minds.