The DX rear mech is classed as not compatible with 11T because it came before 11T and when 11T was released at that level, DX was phased out.
It works, just like M900 mechs work with 11T and they never had an 11T cassette to go with them.
If you hub is 7 speed and you want to put a 7 speed cassette on it, that is fine. As you want to fit a compact 11T one on you'll need a thin spacer at the back to allow the cassette to be clamped up correctly. If you have the old cassette, you take it apart (a few long bolts or crack the rivet out) and pinch the funny shaped thin one.
That usually does it.