I have had exactly the same problem on my 2007 se automatic too. Rather than a jump it's more of a crunching feel, almost as if the car is tripping over itself. Seems to be a fairly common thing. Just be careful of your tyres. Check them regularly because my front right has a big crack in it, and I'm pretty sure it's due to the full lock syndrome. You should never drive with full lock on I know but the steering on the jazz does just kind of throw itself in to full lock if you turn sharply. Try and avoid it though or else you'll need a new tyre like me
:-(