We use time-resolved detection of the Hanle effect and polarized photoluminescence with dark intervals to investigate the buildup and decay of the spin polarization of nuclei interacting with donor-bound electrons in n-doped GaAs. Strong hyperfine coupling defines the millisecond time scale of the spin dynamics of these nuclei, as distinct from the nuclei far from impurity centers, characterized by a thousand times longer spin-relaxation time. The dynamics of spin polarization and relaxation attributed to the nuclei inside the donor orbit is observed on the time scale from 200 to 425 ms.