I'm not really sure I follow, but it sounds like you might have cheated them in using the get command with a count higher than 1 potentially? With them all referring to the same "character", summoning one, then placing one in chest or something might not keep them "saved" as summoned.
Generally:
When you tame them in the cage, get them out and right-click in your inventory, they disappear there and are in the world, able to be interacted with.
You shouldn't have them in the inventory anymore, nor be able to place them into a chest at that point. (unless you interact with them again and press the carry button that'll be available there)
I recommend, in case you did cheat them in with a command, to use the ... i think `/body` command it was? or straight up `/getgen` command with their respective id (not a name or something, just their npc id number) - this should prevent any issues in those regards.
But it might as well be that I misunderstood the issue, in which case I do recommend some further details and clarification to understand the issue better.