I've found myself in the same position more than once. It's also worth noting that it's not always the OP that changes the question.
I agree that your answer should only be judged against the question as it was framed when you wrote your answer. I would prefer that if the OP has a new question (often based on the information that you have provided in your original answer) then they should ask it as a new question. We live in an imperfect world.
If I see an answer that appears to be out of sync with the question, I certainly try to look at the times the question & answer were posted / updated. Personally, I'd probably post a comment rather than downvote, but that is just me.
[Actually, I don't downvote many answers, I prefer to upvote good answers and let them rise above the rest. I'm more likely to downvote poor questions, where I can reverse the downvote if/when the question is improved. (I prefer to downvote questions, rather than closing them, where possible. It seems to me that our VtC process is something of a "trapdoor function").]
When I've found myself in this situation, I've usually edited my answer to include a note that I was answering the original question, rather than the edited version. Otherwise, I could end up chasing the question indefinitely! If people still want to downvote, that is their prerogative.
As for your last question, where the question in the body differs significantly from the question in the title, in most cases I'll post a comment asking which question they'd like me to answer. If I do post an answer, I will simply state explicitly at the start of my answer which question I am answering.