If it is a radial velocity effect, the wavelength error should be proportional to the wavelength ie the error should be greater at H alpha than at H gamma say. If as you say the error is roughly constant in wavelength and given that Demetra is in beta testing, I think I would double checking against a reduction done using ISIS for example in case Demetra is incorrectly measuring the relative positions of lamp and star spectrum for some reason.
Small absolute calibration offsets between internal lamp and the sky are not uncommon though, due to slight differences in the geometry of the light paths and we are talking a fraction of a pixel here so even if the error persists, it may not be anything connected with the star. (Are you seeing it consistently on any other stars?) Measurements of the solar spectrum (eg the daylight sky) can be used to quantify these sorts of instrumental offsets.
Another thing to check is instrument stability. I measured my ALPY to be very stable but changes in temperature and orientation can produce small shifts. Did you measure the lamp spectrum at the same time as the star with the telescope still aimed in that direction? Are lamp spectra reproduceable before and after the observation