I don’t think you need to write it yourself, since there are also libraries that implement specific algorithms for pseudo-random number generators, if if you’re worried, you could pin or vendor the dependency.

But it’s true that if the algorithm isn’t specified then the implementation is free to change it, and probably should change it sometimes, to ensure calls don’t depend on it being fixed.

(Reproducibility is normally about what happens when you use the same version of everything.)