The Doctor tells Grace that in ten years Gareth will head the seismology unit at UCLA, and devise a system for accurately predicting earthquakes, which will "save the human race several times". The movie takes place in 1999, so Gareth will devise this system circa 2009. "The Enemy of the World", a Second Doctor TV story, in which Ramón Salamander comes close to global dictatorship through the use of an earthquake machine, takes place in 2018. Now, in all likelihood, the events of TEOTW are no longer canon, since I feel like that would have come up during the Thirteenth Doctor's tenure if Salamander was that significant a public figure. But I could be wrong.
So the question becomes: was the Eighth Doctor preventing those events or causing them? TBH it's kind of weird that he knew about Gareth's poetry exam at all.