In the current build it appears that when a player selects 'Extinguish' from the contextual menu, whilst holding a water container, the action uses the full amount within the container. However, it would make more sense if there was a specified amount necessary to extinguish and any remaining amount would be residue after the act. I.e. I put out a fireplace with a canteen 100% full but also put out another fireplace with a canteen that was only 85% full (both were empty afterwards). Therefore in the former case, when using the 100% canteen, at least 15% should have remained (assuming that 85% is the proper amount to extinguish the fireplace).
More than likely there is no check, and as long as the water container contains any fluid, then the 'Extinguish' action is available whilst holding said container. This doesn't make sense as there is a threshold amount necessary to extinguish the fire and any left over should be residue.