You may be right about the law in your state, but that's a very odd rule, if so. The jury's verdict in this case merely means that the state hasn't proved Zimmerman's guilt beyond a reasonable doubt. It doesn't mean that Zimmerman proved his justification by a preponderance of the evidence, which would be the standard in a civil case. So I don't see any reason that the verdict in this case should preclude a civil action by the family.
Now, my understanding is that in Ohio (and only Ohio), a criminal defendant must prove self-defense by a preponderance of the evidence. So, in Ohio, it would make sense for a finding of self-defense in a criminal case to preclude the issue being relitigated in a later civil case--the defendant already proved self-defense using the same standard that would apply in the civil case. I don't know if that's the law there, though.