I have the Fiskars Fuse and use several of the Sizzix dies in the Fiskars Fuse. With the correct set up they work without any problems.
The sandwich I use starting from the bottom: the Fiskars adapter(shim) A plate, Sizzix die, up to 6 layers of fabric, Accuquilt Go cutting mat and a couple sheets of card-stock.
The Fiskars adapter plate is 1/16" thick - so I've also used a piece of 1/16" thick Lexan as my bottom shim in place of the Fiskars A plate.
The Sizzix dies are slightly thicker than the Accuquilt dies, so you need to adjust the shims so they roll easily in the Fiskars Fuse. I experimented with how many sheets of card stock on top of the Accuquilt cutting mat to put enough pressure to cut through all the layers of fabric. I usually use about 5 pieces, but if I'm only cutting one or two layers of fabric, I'll add a couple more sheets of card stock.
I just finished used the Sizzix mini wacky web die to cut up 1 full jelly roll and 1 full layer cake. I have just minor cuts in the Accuqilt go cutting mats with this set up.
Hope this helps.