I store them at about 40 degrees in a produce cooler, so mine won't up up until they warm up. I usually take them out around now, inspect them, divide them pretty aggressively .. not so much because I want more plants, but more to have manageable size tubers for pre-sprouting- big clumps are unruly
once they're cleaned up and divided, and ive let the cuts callous over, I lightly dampen the storage media (which will have dried significantly in the ~3months they were stored in cardboard boxes)- usually by mixing in relatively wet fresh media- somehow that seems easier for me to get the right feeling then adding water... when I use water directly I feel like it's messy and hard to get evenly damp and I always end up overdoing it. then I put the tubers back in their boxes into the media vertically, with the tuber buried, but the crown exposed so I can tell when (and which) develop eyes. I check the boxes about every 2 weeks and pot them as they begin to sprout. I cover them/put them vertical instead of laying on top because I can fit more in each box, to encourage root development, and keep them from drying out and make it easy to see which have sprouted with a quick glance. I do go very very light on the moisture to keep away rot..
this way, I can stack their boxes while they're sprouting. they don't need light to sprout, just warm. I go to the local florist and ask them for their empty flower shipping boxes.. they are about 8" wide and 3 feet long, and very sturdy, you can stack them and because they're narrow, it's easy to divide into sections for different varieties so you don't have to label each tuber individually. that's not going to be an issue for you yet.. but when you have a couple hundred tubers and dozens of varieties, it will.
I do have a big wire shelf unit with grow lights on a 3 season porch, so I have a place where, once they're potted up they are protected from low temps, can get good natural light, and with supplemental lighting to extend the photoperiod. they focus on growing feeder roots when days are longer than 12 hours, and fattening tubers when shorter, so you don't need very strong lighting, just long photoperiod (14 hrs) so they develop a good root system when potted up to get best results when moving out side.
if I didn't have that space, a protected outdoor spot with good sun, I definitely wouldn't warm them up this early. oh, in my location, they usually go in the ground mid- to late May, so I'm warming them up 75+ days early and most will have 4-6 sets of leaves before they go in the ground.