If the box has cable clamps then that will prevent the cable moving and becoming loose so it’s not necessarily needed to secure the box but it’s not hard to do, so I’d personally fix it in place , above any insulation if possible.
Yes, the ones I'm looking at have the clamps to secure the cables and the terminal block sits in the middle.
As an aside, is it best practice to keep cables and junction boxes above the insulation. Might be a job, the previous owner installed about two foot of it up there!!!