Shortly after the formulation of special relativity, Einstein's former math professor Minkowski found an elegant reformulation of the theory in terms of the four dimensional geometry that we call today Minkowski space. Einstein at first rejected the idea. (`A pointless mathematical complication'.) But he soon changed his mind and embraced it full heart, making it the starting point of general relativity, where Minkowski space is understood as the local approximation to a 4d, pseudo-Riemannian manifold, representing physical spacetime.Other make this argument that relativity implies a eternalism philosophy of time. I disagree with this argument. You can talk about spacetime with either Galilean or Lorentz transformations. If that is eternalist, then it is either with or without relativity.
The mathematics of Minkowski and general relativity suggested an alternative to Presentism: the entire 4d spacetime is `equally real now', and becoming is illusory. This I call here Eternalism.
Note that Rovelli is compelled to make his relativity story all about Einstein, even tho he had nothing to do with the issue at hand. Minkowski did not reformulate Einstein's theory, as it is not clear that Minkowski was ever influenced by anything Einstein wrote. Spacetime relativity was first published by Poincare, and Minkowski cited Poincare.
Rovelli ends up wanting some compromise between presentism and eternalism, as both views are really just philosophical extremes to emphasize particular ways of thinking about time. This might seem obvious, except that there are a lot of physicists who say that relativity requires eternalism.