Yes - if you pre-pay your gratuities (which we always do - SO much easier!), it includes everyone on the boat. The only time you would give extra is if they gave over-the-top service.
On Avalon, we have had excellent service, but there have been a few that have gone out of their way. For instance i had asked for a specific after dinner drink the first night of the cruise, but they didn't have it, so i had something else. The next night i went to the lounge after dinner, and the bartender came over and told me that he had gone into town that day and gotten the items needed. He handed me my drink for free that night as an apology for not having it the night prior! I was stunned. Needless to say he definitely deserved, and received, extra on that cruise!