Not on my watch, he will or he won't?

I was writing a story where Boy A was trying to confess to Boy's B sister. And Boy B doesn't like the thought of that, so he tries to keep his sister away. He overhears someone saying that Boy A will ask his sister out today and Boy B goes,

"Not on my watch, he will." I'm thinking if this makes sense, or should I replace 'he will' to 'he won't'. Either way, I always end up being confused whether to use he will or he won't in different scenarios. Can someone clear it up for me?

Another example I tried fiddling with was this:

The cat was going to puke on my bed and I yell, "Not on my bed, you will/won't!" Should I use will or won't?

The phrase is more idiomatic if the verb at the end is negative. So "Not on my watch, he won't".

Likewise "Not on my bed, you won't". The sentence would also work with "don't" instead of "won't", as if the speaker is referring to what the cat is actually doing rather than reacting to the cat showing now that it plans to do something in the future. But, either way, the sentence strikes me as stranger than your first example, because you don't expect the cat to understand your words.