My tumble dryer does seem to magically de-crease clothes, it gets them basically as smooth as they come from a shop and smoother than they ever do from me ironing, but actually I put something (dry, clean, creased) in it on a "refresh" cycle which is supposed to uncrease and it did nothing. I had to put it through a wash cycle first.
I have also found that if I leave stuff in the washing machine too long and then tumble it, it still looks creased, although nothing NOTHING like what it used to look like when I left stuff in the WM for 3 days and then tried to hang it up.
So actually, I think it's less "magically de-creasing" and more "encourages behaviour that is less likely to form creases"
I think the secrets are:
I have a vv modern dryer and I specifically selected it for non creasing. Apparently the shape of the drum and a spin which changes direction can reduce creasing.
It's a heat pump dryer. Again apparently v good for non creasing.
It's separate from my washing machine, and has a higher capacity. I can dump the whole wash load in without halving it and there is plenty of space.
It's much easier to pull a load out of the TD than it is to empty an airer, and put a new load into the TD than fill the airer. So I very rarely leave my washing sat in the machine for days any more. It's typically max 12 hours. Occasionally up to 48. Washing sitting around wet causes creases, so moving it over ASAP is key.
Again removing from TD and folding/hanging ASAP also helps prevent creases. If I just pull the stuff out of the TD and leave it in a basket, it will be a bit creased (but not as bad as what I used to get from the airer) If I leave it in the TD for 12-24 hours or longer it will be a bit creased, again not as bad as airer creasing.
My TD also has an anti-crease protection thing where it pointlessly tumbles things every 15 minutes until you empty it. I sometimes turn this off without emptying it, it doesn't seem to make any difference and is just a pointless waste of energy.