Yeah, you're only going to hear the click on the right swivel bar. But like Kanedas Bike mentioned, the right and left bars do move in conjunction with one another, so locking the right is the click you're after and will lock the left as well. But as I said earlier, there may still be a little swing remaining, but it should be a whole lot more secure now. Besides, that's how you're really supposed to transform it.
Also, perhaps I may need to mention that when swinging the bars forward, you should move them together as if they're one piece.