When you're "on watch" it means you're staying awake to guard and make sure things are OK while others sleep. You all take turns to be on watch. Think of a situation such as camping in the wilderness, or in a war zone, where your group may be attacked. You'd say "Not on my watch!" if you hear of something you disagree with, and you won't let that happen while you're around. "He uses a lot of chilli when he's cooking." "Not on my watch!" "Green pants go with a red shirt." "Not on my watch!"

not on your time or while you are in charge.. not while you are the responsible...

Whatever you dont want to happen, it's not gonna happen while you are there !!! NOT ON YOUR WACTH !!!

it means "someone distancing themselves from a situation" cowboy...

It means the same as 'not when I'm in charge'.