No, you do not.
The $12 per person per day is a gratuity that covers your stateroom attendant, your waiter, your assistant waiter, and the head waiter.
So unless any of them performs above and beyond, in which case you can provide an additional gratuity, you don't need to do anything more.
On the flip side, if they do not perform up to your expectations, you can always go to the Purser's Desk and ask to have the service charge reduced.
So don't feel like you do not have any control over the gratuities.