It is now mandatory for you to have a blockchain.info wallet. We simply have too many issues regarding people paying from the same wallet vendors to same wallet vendors. We've made an adjustment on your accounts page so that you can indicate which bitcoin wallet vendor you are using. Please make use of it.
You can still use whichever wallet vendor you choose to, we won't accept any more support related issues regarding payments not going through if you decide not to use blockchain.info as we can not fix that for you.
As stated previously, we rely on the safest platform in the world, the Blockchain, to do the transaction confirmations for all your transactions. Each transaction should have a unique transaction hash id for this to work, some bitcoin wallet vendors bundle transactions, we can't cater for that, it is simply not possible.
How to Set Up a Blockchain Wallet Address
Since the Blockchain is just a Wallet, where you can only send and receive Bitcoin, you will also need a way to add funds and withdraw them, when you are ready. For this you can use your other Wallet Vendor, such as Coinbase, etc.