The grid failure in Spain and Portugal has nothing to do with "spinning turbines".
The turbine type is not relevant for fast reaction, and no, a nuclear plant does not use the same turbines like a gas plant. Perhaps you should look up their construction. A gas plant turbine basically looks like a jet engine.
Nuclear plants will never be super fast in reaction. They are good enough for load following, so no one really cares, and with steam reservoirs you theoretically can react faster, too.
That nuclear plants are always slow for load following is btw. a misunderstanding. Most of the french ones do load follow, but in a specific way. That means one plant that is lowering its output, will continue to do that, every time when it is required that "some plant" lowers it output. Until it is at the lowest point, then it changes its role and comes into the fleet that is ramping up. The french plants are designed to be able to make two full cycles of shifting down to minimum and then shifting up to maximum again, two times in a day.
On the other hand, the German plants, essentially very similar, are not designed for that. They always just were base load plants.