Do I have to do anything to pair my DBS Altitude Card to my existing Multiplier account or is it automatically linked?

Any credit cards under your name can be seen on the ibanking portal home page as it's own "account". From there, you can see all the transactions much like a normal bank account (though it usually takes a few days for you to see the actual transaction)

When the payment is due, you can choose to pay using funds from your multiplier account.

Eligible transactions from any DBS / POSB credit card under your name will add towards your monthly transaction under the bank and earn tab.

I hope this helps

Short answer, it is automatically linked as long as it is opened under your name. The system is smart enough to recognise it.

To make sure, you can go POSB iBanking site, go to "My Account" tab, click on the "Bank and Earn Summary" and it will give you a snapshot of your Multiplier account and any automatically linked credit card.