Your excursion(s) and tips will be billed to your onboard account, which is settled at the end of the cruise.
Many people like to deposit extra funds (by calling
DCL) in their account before the cruise (for example, some folks call it prepaying gratuities). You could do that if you want to "pay" ahead of time. It just becomes a credit balance on your account, and all is settled with either a final charge to your payment method, or a refund of there are funds left over.
But, for many, it's easy just to let the bills pile up on the account (gratuities, excursions, drinks, bingo, etc...I have a list now of over 50 things you can spend money on) and just have it all charged to a credit card when it is all over. DCL makes it easy to spend lots of money on your cruise