As above, you need an interface between your controller – mixer – laptop.
I have an X1 and it’s a lovely piece of kit, barely used it though as like you I’ve not currently got a mixer I want to use it with. I have the NI Audio 2 soundcard into the mixer on my controller, which does its job but I instantly regretted not getting a proper one; it’s like a crappy little plastic thing designed for people who want to DJ with an iPad really.
Tale Of Us use (predominantly from what I’ve seen) a Xone 92 with Traktor X1s and CDJ timecode CDs, connected up with an NI Audio 8 (bear in mind there’s two of them so 2 channels each, an X1 each, and a laptop (presumably midi clocked to each other) each. This would probably be my ideal setup, but I’m forever experimenting and saving for/buying new gear.