I plant mine shallow not more then 1/2", so that when they wake up they shoot little sprouts out of the soil that are pink. They will do it even in totally dry mix.
When you dug them up you should have noticed sharp tips on corms: that's the up side. The bottoms are flat, they sort of flake of dry in spring and you should see light colored firm bottom, not soft not brown.
They sprout roots from the top of the corm , so once they have started they need like an inch or so of mix above them to keep the roots moist for the rest of the season (as the top dries up fast). I then sprinkle more mix on top if I see that they are too shallow.
I don't dig them up every year: they will dry up too much if stored dry. So they recommend to put them in dry peat until spring. It's too much to bother for me.
If they don't have pink tips you should put them back in pots for now: it's too early to start them up. I'd say March at the earliest unless you are in Deep South.
So my big ones i usually start up on heat mat in clam shell in moist long fiber NZ sphag all covered up loosely. And you then need to carefully remove sphag for planting as the roots might break.
This is the pic of my corms sprouting : roots from LF sphag , ready to be planted:
The rest (in pots ) I start up by just watering lightly to moisten the mix a bit and keeping them in the sunny window to heat thru. They will take at least 4 weeks to wake up and show some signs above the surface:pink tips.
Then you can start watering slightly more until they grow a first leaf , then water a bit more still. It is sort of like starting Callas or Amaryllis.
