Comparing wheel stories, how sad is that?
I've lost count of the number of wheels I've seen received on pallets, worn to limits and then some, with gaping cuts in the tread, fully inflated and stacked 2 high. Via air transport! So much for proper handling of dangerous freight....
Regarding care of parts while WIP, you can go completely overboard but as long as a few sensible precautions are taken you're generally all right. Segregate everything into the same wheel set and keep it together is #1 fairly obviously. Bearings are sensitive and the easy way to prevent damage and corrosion is to put each cone into a thick plastic bag. Other parts are fairly robust and can be placed together in a plastic parts tray to keep them together. Common sense is an essential factor in handling wheels being serviced, though wheel cleaners are not always the intellectual elite of the maintenance world and a lot rests on the shoulders of the parts inspector to ensure everything is not only satisfactory to the manual, but as you found, the right part in the first place! It's not always as obvious as incorrect tiebolts either. I'm aware of at least one lost ATR42 mainwheel due to the incorrect P/N outer race being fitted (there are 2 standards with different cone angles, visually almost identical and only identifiable by P/N).
As with so many things in this business accuracy can be the difference between life and death, even in a supposedly simple and unglamorous area.