Just hit input on the remote until you see auto appear. Not sure what you mean by "will DTS play in other mode besides the DSP ones". DTS will only play when a DVD has DTS encoded in it. You normally have to manually select that option within the DVD's menu. By setting your receiver to Auto, it should automatically pickup up the DTS mix and play it as such, after you have selected DTS on the DVD's menu.
You cannot play a non-DTS DVD in DTS. You can play non-DTS movie/music in DTS Neo 6 music/cinema. For instance, you can watch any TV show on any channel in DTS Neo 6 but you can't watch that same show in DTS. I think you may be a little confused on how DTS works, or maybe I am?
Shinerman