There is nothing magical going on here. You get the same problem if you just leave off the 'exit' from the code to be run by the child.
The only trap that 'eval' allows here is that, if the child 'die's, then the 'exit' can be skipped. If there is no 'eval', then that causes no problem because the child still exits without returning to the calling code that is meant to only be run by the parent. But with an 'eval', the 'die', in effect, transfers control up to the calling code and you end up with both parent and child running the calling code.
The only sharing is the standard sharing that happens when you fork. That is, the child gets a copy of (nearly) everything from the parent. Nothing is shared from the child to the parent (the exit status and resource usage is made available to the parent and output from the child can go to the same destination as the parent's output, of course).
Does that clear the mystery up for you?