When playing with the water carrier do the player give water from his own cantina?
Yes, any share of water drops one player's canteen by one, to raise someone else's canteen by one.
The Water Carrier's special abilities are:
- can share water with players in adjacent spaces, doesn't need to be in same space
- can carry just a bit more (max is 5)
- can draw water from already exposed wells, for one action
Nowhere in the rules does being water carrier change how sharing water works, just makes it easier for that player to do so. Whenever you share water, it's a trade, not free water.