The purple box represents the bounds of the simulation, anything inside that box is what gets simulated. Go the flipsolver node and under the 'Volume Motion' tab open the 'Volume Limit' tab, from there you can toggle off the preview of the box as well as control the sizing. You can also use this bounding box as a collider, click on the fluid object node and toggle 'Closed Boundaries'.
If you wish to only see the melting cube while also playing with parameters, you can pin the viewport to the obj level. Go back to the obj level and toggle off the display of the AutoDOP node, and only keep the display on the 'box_object1_fluid' node. After that click on the pin icon (see image) to pin this viewport. Now if you go inside the AutoDOP again the viewport won't change and you'll be able to play with parameters while also viewing the mesh version of the melting cube.