Just as BoomBox said check the output routing.
To answer one of your questions above: No, you dont need a splitter or anything. Mixtrack Pro has inbuilt soundcard so it saves you from all this things.
As your controller works in vdj as intended then it’s not a fabrication fail or something. So just mess around with the output, check your mapping for the 2 cue buttons (above the Laod A/Load B buttons) if they are mapped correctly and do what they supposed.
Good luck!
Ps: Test default and/or get a mapping from traktorbible or djtt and try with that, too.