The unusual dependence of femtosecond laser writing on the light polarization and direction of raster scanning is demonstrated in silica and chalcogenide glasses. Two different mechanisms contributing to the observed anisotropy are identified: the chevron-shaped stress induced by the sample movement and the pulse front tilt of ultrashort light pulse. Control of anisotropies associated with the spatio-temporal asymmetry of an ultrashort pulse beam and scanning geometry is crucial in the ultrafast laser machining of transparent materials.