This is a good question.
Imagine BTC to be a public safe with a lot of lockers like the ones you'll find at trainstations sometimes.
Everyone can see the safe as well as the lockers but only the guy with a key can access the locker and use what's in in.
Same with a distributed ledger. Everyone can check it out, all the blocks, all adresses and the Bitcoins attached to it. But only if you have a private key you can actually sign transactions to move BTC to another adress.
So your BTC will always sit on the distributed ledger for everyone to see, but as long as you are the only one with the private key, you alone have the authority to move them around.
Ckeck it out:
https://btc.com/
click on a block hash to see all transactions
TL;DR: The private key has all the power. Not your key (because you left BTC on an exchange), not your coin.