Rubber Embossing mat help please

Ive recently bought a die cutting machine, it cuts the dies I have well using the plates, but I bought a die for a pillow box, I feel the folds can be more defined. Do I need a rubber embossing mat to do this?

I often just add a sheet of card between the cutting plates over the die. I did buy a rubber mat but ended up accidentally cutting the shape out lol!

Sounds like the kind of thing Id do! Thanks, Il give the card idea a go.