Most (not all) fungal spores are exceedingly mobile, very tiny spores blowing on the wind. So if you have the right conditions, it can just start growing. Since what you see is just the fruiting body, sometimes the fungus was there for years before growing in the ground, and it was just teh conditions that brought it out. Recent conditions have been ideal for fungus fruting - warmth and stress for rather dry August-Oct followed by tipping it down with rain, and little frost year, and if you go for a walk in the woods you'll see loads just now. Normally this fruiting frenzy happens earlier in the year.

But it can also happen that you bring it in, if there is fungal growth already in the material you spread. Someone I know collected leaves from the woods for composting, and got some unusual woodland fungi the first year or two.

The only common thing your description suggests is Orange Peel Fungus, as Spider suggests. There are some similar things, but we'll need a picture if we are to suggest anything else.