The Enterprise had a slight head start, but the Vengeance was able to catch up to it because the Vengeance was travelling at a faster speed. Plain and simple.
Your point about the warp bubbles of the two ships is irrelevant. As @Hypnosifl and @JamesSheridan mentioned in their comments below your question, there are many instances in Star Trek (across the series, across the films) where it is clearly shown that (a) a ship travelling at warp can see the immediate universe outside the bubble, and (b) that ships can exchange fire while at warp. (Think about the desperate attempt to flee the Borg at the end of "Q Who".) It might be interesting to compile all such instances...but perhaps only mildly so.
Star Trek may occur in a technologically-advanced future, but this particular topic is less to do with warp field mechanics and more to do with Newtonian kinematics (or even earlier, Aesop's "The Tortoise and the Hare" --- not directly analogous to the Vengeance / Enterprise chase for obvious reasons, but lessons to be learned about speed and winning a race, nevertheless).