It is hard to say where it goes wrong from the screenshots. If you can upload the file someone can have a look at the model to see where it goed wrong.
First thing might be to make the insert non-penetrating to the housing. Second is that your constraints are too rigid (unless the box is glued to the mating part.) Try making that roller/slider and restrain one top edge and one side edge to keep it floating away.
Did you use a force or a pressure? What's the application?
Thanks for both of your answers, I got a sensible result eventually, think it was two things: Using a contact set (bonded) rather than relying on the default global contact and Also having the correct poisson's ratio plugged in for the material. I used a force applied to the face as shown in brown arrows.