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Here's what you always need to keep in mind when dealing with any crypto currency, including EOS. Whoever holds the private key of the wallet where the coins are stored owns those coins.

When you leave your crypto with an exchange, they basically own them and not you, since they hold the private keys and not you. That's why, you should never leave your crypto except on a cold/hardware wallet that only you have access to its private key.

Remember, tokens are never actually stored in any wallet as such, they live on the blockchain, that's the whole point. What lives in your wallet is the private key which can decrypt that wallet and allow those coins to be sent to another address on the blockchain. So your wallet actually holds a key and not the crypto themselves, as those reside on the blockchain.

So, to answer your question, yes, you need to move those EOS tokens from any exchange to a wallet of your choice which supports ERC-20 tokens. You can use https://www.myetherwallet.com/ (known as MEW) for this, but preferably buy a Trezor cold wallet so that you could unlock your MEW wallet safely with it, and that way, your private key for your MEW wallet would be safely stored on the Trezor device which is extremely difficult (if not impossible) to remotely hack (unlike a computer or a mobile device).

Once you move your EOS tokens to your MEW wallet, you need to map your wallet's Ethereum public address to your EOS public address as I explained in my original post. If after some time you decide to move your EOS tokens to another wallet, you'd then need to repeat the same process, otherwise they would be mapped to a wallet that no longer holds them, and you would therefore lose them when the ICO comes to an end.

Thanks @zedchamaa. Really appreciate your answer. I am moving my tokens to private wallet.

But don't you think that (except the secutity issues that you underline) as long as you can trade your EOS on the exchange at the main rate they are mapped on the public eos adress?

No they're not, you have to map your EOS tokens to your own public EOS address which gets randomly generated, otherwise, you won't be able to use the EOS tokens once the ICO has ended: https://goo.gl/TSq52F

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