In sit-down restaurant, whose responsibility is it for you to get what you ordered?

When I order something, either as-is or with some reasonable modifications that the server says are ok (e.g. not putting onions on something, versus asking to remove something from a soup), if it comes out incorrectly, whose responsibility is it? Who is supposed to check the food to ensure it matches my order?

In other words, if the food is incorrect, am I correctly adjusting the server’s tip downward, because now I have to wait longer due to poor service (wrong order provided)? Or, the server provided good service by politely taking my order and politely offering to have the kitchen correct it, even if now I have to wait longer for my meal due to no fault of my own, so I should still tip the customary amount?

If it’s the cook’s responsibility to make sure that what lands on my table is what I told the server, it seems unfair to dock the server’s tip. And, do food runners have any accountability in this process? If so, does it matter whether the server shares tips with them?

I’m trying to make sense of where my discretionary tip fits into the restaurant employees’ scope of accountability, since I’m being asked to directly pay part of their compensation.