Uh...
This happened: A starts a war W with B. As a follow on effect, some groups inside B starts a civil war W2 with others in B.
You say that A is responsible for the second war W2 too, which they didn't start and even actively tried to stop?!
After the war, when does A stop being responsible for everything bad that happens to B, done by B themselves? After 10 years? 100?
You just blame A for everything, including the weather? :-)
(It is easy to make a good argument that the W2 war would probably have happened anyway, at some point. Or that Saddam was already doing a continuous civil war with his army/police against everyone but his supporters, to keep power. You might even argue, but not with your definitions, that USA is responsible for all those killed by Saddam when they didn't topple him in the first Gulf war...)
Edit: Clarity.