Uhm, let me see. Sound should run from your turntables to your DJS1 inputs. The DJS1 outputs should run to your mixer. And clearly a USB cable fromDJS1 to your laptop/computer. I am not sure what you mean when you say your signal path is tt -> djs1 -> mixer -> djs1. That seems impossible to me.
I don’t have my gear with me, so can’t check (and I don’t do DVS with Serato, or at all actually, but I know how it works in my Mixvibes Cross setup), but I am assuming there is an easy button to click that let’s you switch between DVS and thru modes. In through mode the sound from a regular vinyl goes into Serato and rather than being considered timecode signal is routed straight “thru” to the DJS1 outputs.
In Mixvibes Cross for example it’s a button right in the decks section. One mouse-click switches it. I am pretty sure you can even map a button on your controller to do the same.