Neo:6 would suggest it's getting two-channel and processing it to create surround, just like Pro-LogicII/IIx does with stereo material.Neo:6 is, in very general terms, the DTS version of PLII/IIx - in other words it's creating sound, not decoding it.
That would be fine from stereo TV on Sky - after all, stereo is all you're getting over the HDMI - but not for DTS or DD 5.1 soundtracks on DVD or Sky Movies.
You can change this mode by pressing the surround button on the Onkyo remote, and the receiver should remember the last setting you chose. Personally, I use PLIIx Music for most stereo TV viewing, as I find it gives the most natural results.
You should be outputting bitstream from the player - let me know what the player is and I'll do some hunting.