If I understand correctly, DGD pays you a small free on all digix gold trades. Now, what happens when you deposit your DGD in an exchange? The DGD is still yours, so you're supposed to receive the dividend, but obviously it goes to the exchange instead. Wouldn't it cause a massive withdrawal/deposit movement surrounding payment days?
This is an issue with tokens like DAOTokens and DGD Tokens right now - both in terms of how to obtain them (during the token sales) and in terms of storing them to collect rewards. The issue lies with (1) people using exchanges as storage and (2) exchanges not having the mechanism to read and send tokens associated with an Ether / Exchange account.
If you want to receive tokens during a token sale, use an account that you (and only you) have the private keys for.
If you want to receive rewards, use an account that you (and only you) have the private keys for.
In the future, exchanges may start having ways to read, send, store, and collect reward tokens for individuals, but until then you need to have your tokens in your own account to collect rewards. Even if an exchange supported this functionality, I still would not trust the exchange over my own account that I control 100%.
Tokens are associated with an address. That address can be accessed via a private key. If you don't have the private key then you cannot directly access your Tokens and your ETH.
What people need to understand is if you do not have the private keys to the account, then the account is not yours. It is the exchange's account, or whoever holds the keys.
You can hub-bub around all you want and say that it is yours and that you can withdraw whenever you want, but look at a situation like Mt.Gox, Cryptsy, and all the other insolvent/hacked/exit-scam exchanges and the reality is they are not yours.
There were so many people who sent directly from an exchange to participate and obtain tokens and (without adding additional data--data that basically said "Hey! Don't send the tokens back to the address they came from! Send them to this new address instead!) people did not receive their tokens, the exchange did.
The same is going to be true for rewards: in order to receive rewards or dividends or whatever you want to call them, you must have the DGD in an account that you control and have the private keys to. If it is on an exchange, the exchange will receive those rewards instead, just like they received heaps of tokens during the token sale.
Furthermore, in order to interact with TheDAO contract (voting on proposals, etc) and the DGD Contract, you need to have an interface that allows you to do so. Exchanges do not support this functionality either.
Keep your DGD and DAO Tokens in an account you created using Mist (Ethereum Wallet), interact with it via Mist, and only send to an exchange when you want to immediately exchange them. It's safer, it allows you to actually participate when votes occur, and you always have complete control of your funds.