We use N-body simulations to study the effects of tides on the kinematical structure of satellite galaxies orbiting a Milky Way-like potential. Here we focus on the evolution of a spherical, dark matter dominated satellite, which is modelled with two stellar components set ab initio to be spatially and kinematically segregated, in a way that resembles the configuration of the metal poor and metal rich stellar populations in several dwarf spheroidals of the Local Group. We find that an important attenuation of the initial differences in the distribution of the two stellar components occurs for orbits with small pericentric radii. This is mainly due to (i) the loss of the gravitational support provided by the dark matter component after tidal stripping takes place and (ii) tides preferentially affect the more extended stellar component, leading to a net decrease in its velocity dispersion as a response for the mass loss, which thus shrinks the kinematical gap. We apply these ideas to the Sculptor and Carina dwarf spheroidals. Differences in their orbits might help to explain why in the former a clear kinematical separation between metal poor and metal rich stars is apparent, while in Carina this segregation is significantly more subtle.