> I wonder if Americans know how much of their society and culture bled incompletely into other countries via movies.

As with anything, it depends. I'd never heard specifically of your Tylenol example, though I'm generally aware of the idea that (pop-)cultural references often won't be understood when viewed/heard by audiences with different cultural context.

But I think many people in the US just don't think about it, because they don't need to and it never occurs to them. If you told them your story, they'd just think "huh, that's funny; makes sense, but I never thought about it that way".