How the ID works isn't actually described. But let's go for maximum fun.
The ID is like a hermit shell crab. That brain on its back? One it took from someone.
It wears your brain like a hat. This is where your mind, memories and soul live. You are dead, and trapped in your own dead brain. It has complete veto over all of your actions as it is wrapped around all "IO ports" of your brain.
Over time it digests your memories and becomes smarter. But it isn't very good at social intelligence, and devouring your morality and the like would get in the way of eating more brains. So when disguising itself as you, it actually lets your soul and mind do things; it magically knows what you are about to do, and steps in and takes over whenever you do something out of line. Then it edits your mind a bit to make you not do that any more.
In an antimagic field, it is still in there, but it isn't as fast at intercepting your actions, nor can it further digest your memories, nor can it edit your mind to avoid you doing it again.
This means whenever the "trained mind" it has in the skull does something it doesn't want it to do, it is slower at stopping it, and the resulting behavior isn't as smooth.
Not every mind notices this. A well "trained mind" can continue to do what the intellect devourer wants without ever noticing that it has increased control. It may continue to fool its companions because it is broken to the harness. If it did try to say "I'm possessed by an intellect devorerer", it could probably get out the first two words before the devourer could take over, and the devourerer in direct control would be forced to act strange not having full access to its backpack-brains mind.
All you tell the player is "you feel a strange headache" when you walk into the prison. That is the only clue they get. As a player, they get to say if their character is broken to the harness ... or not ... by the player's choice of actions.
