Does Loot Redistribute Among Storages
Lionwaffles is somewhat correct. Storages and th have a percentage of your total amount of resources, therefore whenever the amount of that resource changes, the total amount in each storage will update. So collecting loot from collectors, spending loot on research/spells/troops, losing loot from getting attacked, and gaining loot from attacking will all cause the amount of loot per storage to update.
Source: personal experience (tested it in game)