I leave them folded in a box. I buy them like 10-15 at a time (when they are on sale) and keep them cool (chillin') in the box. Perhaps some talc to reduce rot and such... But no... Just leave them folded.
Certain brands and rim combos can be issues when first mounting. Sometimes, knowing which rim/tire I am replacing, I will pre-mount the tire without a tube and let it sit overnight to stretch before trying to pop the tire on with a tube... But this is rare. And typically only happens with 20mm or smaller width tires
Just store them in the box, it's simplier that way. I have one I keep stored in my seatbag for emergencies. There's no need to put them on a spare rim with some air because they have kevlar beads their going to be limp.