The problem is that this stuff is baked in to the Styler/APP integration. Styler is not really designed for accurate CMYK work, it supports RGB and CMYK as a side-effect.
The colours are not APP's fault, so there is no easy one-shot fix in APP edited source. There are a number of instances where Styler is assuming and using RGB colours. For one example look in $EDITOR/app/libs/APPStyler/_app.3ns, method "StylerForegroundColour". It is defaulting to #000000, and is not drawing the default from anywhere else. Presumably the rest of Styler does similar things, so you have to patch up each and every instance.
One interesting note during my investigations is that there is a template.options JS attribute where you can set up some colours, default padding, etc., but I don't know how or even if you're meant to use that. Perhaps a trip to PTC support may confirm if there is a simpler way to override colouring in Styler.