The output Q' is the complement of Q, which means it is always the opposite of whatever Q is. In other words, Q' = NOT Q. As such, Q' does not take part in the operation of the flip flop, it is simply determined after the operation is complete by inverting whatever value Q ends up with.
If you want to think of it in terms of logic, pretend the flip flop doesn't have a Q' output at all, just the normal Q output. Now put a NOT gate after the Q output. The output of the NOT gate will be Q'.