I have no idea how the automatic tips are distributed on Princess crusies (other than the $3.50 and $6.50 split between the room steward and waitstaff), but having just returned from a cruise on Island Princess I can tell you every crewmember I encountered was there to please the passengers. It didn't matter if they were a room steward, waitress/waiter, cocktail host/hostess, or maintenance person. They treated everyone as they would the captain. I feel the tips were well deserved.
One of my traveling friends saw a lady who was very upset at the cashier in the store because she wouldn't give her a free set of playing cards for the cardroom. The cashier tried to explain to the nasty person that she couldn't give her a free deck of cards from the store, but would ensure cards would be delivered to the cardroom. The passenger was very rude and was never going to sail with Princess again. (No loss, as she seemed to be a real angry person who could never be satisfied.) Even though the cashier was not on the tip system, she made sure cards got delivered to the cardroom. My buddy warned the person delivering the cards that the lady wanting the cards was not a nice person.
The pursers on Island Princess did all they could to take care of the passengers. On the next to last day there was a long line at the Pursers desk. The Assistan Purser was out front getting copies of room charge statements for people that were only in line for those.
I was out on deck one morning watching the day go by and a crew member trying to clean the glass on a door. It didn't matter where he was in the cleaning process, when a passenger came to the door he stopped what he was doing, opened the door and said good morning with a smile on his face. What should have taken a couple minutes took about 15 minutes. Never once did he have a sour look on his face or roll his eyes as some people came out on deck and went right back inside.
I know I didn't have interactions with every crewmember but enought to know they were there to please the passengers.