Picture a whole bucket going over in one movement: not a trickle, not a careful pour, but the lot at once. That single image carries the word. Aim the bucket at a person or a cloth or a bowl of and the result is something completely wet. Aim it at a fire and the result is a fire that has stopped. Keep the second result but take the water away, and you are left with a candle going out. The picture is a way of holding the uses together, not a claim about how they grew.
From the word’s history
The source says douse is probably of North Germanic origin, related to Swedish dunsa and Danish dunse, words for falling heavily or thumping, and points to Old English dwaescan, to extinguish. It marks this as probable, not certain.
來源說 douse 可能來自北日耳曼語那一支，和瑞典語 dunsa、丹麥語 dunse（重重落下、砰一聲）有關，並且提到古英語裡有個意思是「熄滅」的 dwǣsċan。來源自己用的是「可能」，所以這條線索只是線索。有趣的是它剛好對上那個畫面：一大團水砰地落下去。
Wiktionary entry for douse (etymology 1), packet source_ref kaikki:3f6f69a190036ae4:638213673:10882
登入就可以看每一支怎麼連回核心畫面。