Is it when another creature dons the control amulet?
Does the original owner have to expire first?
Is control transferred even if the control amulet is stolen from the previous owner?
The exact scenario is the party has encountered a goblin with a Shield Guardian. They used 'Command' on the goblin and made it 'give' the amulet to them. Does control of the Guardian switch to the player immediately when they don the amulet?
RAW - Immediately
As an earlier part of the monsters description describes that the amulet can be given away, traded, etc, it's fairly clear that the previous owner has no command or attunement time (like many magic items in 5th edition). And a tweet from Jeremy Crawford confirming no attunement.
PS - RAI, also yes