A key thing is that with nukes or any large artificial blast, the energy is pretty much released in a compact area right out into the open. With earthquakes, energy is spread across large areas and often starts far underground, yet still causes damage over a very extensive area. This is part of why earthquakes are much more energetic then man-made blasts.
Large explosions (especially nukes) do produce earthquakes and minor seismic movement, but it just doesn't compare to the comparative megaton-equivalent forces that natural tectonic movements create underground during really notable earthquakes, just like the one being "predicted" in the article above.
Now, to use such a weapon to cause a stress-relief earthquake, some factors need to come into play: Depth at which the device should be detonated to optimize stress relief without causing surface damage. detailed seismic imaging and rock mechanics studies. Geometry of the fault zone.
Even w/ a Castle Bravo type test, massive radioactive fallout would occur in groundwater as well as air. There's also the chance that such an event would cause local volcanic activity.
I thought of mentioning Castle Bravo or Tsar Bomba as contray examples of my general argument, but I simply stated "normal nuke". Neither Bravo or Tsar were at all normal nukes and especially by modern design standards that focus more on the multi-kiloton range and precision-guided multiple strikes against a given area target.
Even with those insanely giant old bombs, I wouldn't absolutely be sure that they'd achieve a massive tension release, even in a fault as tense as the San Andreas. Such a thing is likely just a bit too variable-prone to model effectively.
As for something like a Hiroshima type bomb doing it, bloody unlikely. The original post comment simply mentioned a bomb so I didn't want to stray into the biggest mega explosives of human military history.