The dielectric permittivity tensor for incommensurately modulated phases in insulating crystals is considered. The main attention is paid to the spatial dispersion giving rise to optical gyration effects and the influence of the modulation phase on those effects. General properties of the dielectric tensor are analysed in relation to the lattice and incommensurate superlattice periodicity requirements, the Onsager principle and the condition of absence of the radiation losses in the optical medium. The structure of the microscopic components of the tensor and a macroscopic averaging procedure for the plane-wave modulation region are discussed. The possibility of existence of an anti-Hermitian part in the dielectric tensor of lossless incommensurate crystals originating from the modulation-induced spatial dispersion is revealed. The performed analysis shows a necessity for introduction into the constitutive equation of the term including spatial derivatives of the optical activity tensor.