If it's not clear still, here's how it works.
The spin on a cueball can actually change the speed it's travelling after it touches a rail. I didn't used to believe it, but a cueball can actually leave your tip travelling at, say, 10 miles per hour, and then hit a rail with running english and boost up to 12 mph (random numbers, but you get the idea). Some of the sidespin is transformed from rotational speed to travel speed. I used to think the spin only changed the path the cueball took, but it actually alters the speed too.
The exact same thing can happen if you turn it around: A CB can approach a rail with reverse spin, and instead of coming off at 10ish miles per hour (as it would without spin) it will lose a lot of speed and maybe drop to 5 mph.
I'm almost positive what happened in your example is that when the cueball went from the 2 to the rail... it didn't move 'downhill' towards that diamond as you've drawn it, it went somewhere to the right of the line... either directly perpendicular to the rail or leaning a hair towards the short rail on the right. In that situation, the CB will definitely die with left spin.
You might think "but I hit center left, it shouldn't go 'forward' like that into the rail, it should move towards that diamond"... but unless you hit firm center left, the cueball rubbed against the cloth as it was travelling and started to roll, so that by the time it hit the two, it had natural forward spin.
In addition, there can be the effect the other guys are describing where the shot has leftover forced topspin when it arrives at the rail. There are two flavors of follow/topspin: The kind you get when a cueball stops sliding and starts just rolling naturally, and the kind that is forced where the cueball is actually spinning faster than it's moving forward... think of a tire burning rubber.. the car's not moving forward very fast but the tire is spinning rapidly and the speedometer thinks it's going 60.
When you have that kind of forced spinning action, the cueball can hit the rail and still want to be spinning towards the rail it just left. The spin fights against the cue ball's urge to bounce away from the rail, and they sorta cancel each other out and it just dies. To illustrate this, set up a hanger in a corner pocket, off to the side of the pocket rather than in the middle of it. Put the cue ball 8 feet away, and just smack it hard with loads of topspin. Try to hit between the object ball and the jaws of the pocket. The cueball hits the hanger and loses some speed, hits the rail immediately after and tries to rebound back to you, but the topspin is still there and it either dies, bends forward, or even bends forward and smacks into the rail a second or third time before dying.
The solution in your case would be to hit a bit low (with your left spin also) to ensure that the cueball doesn't pick up that natural rolling topspin... and actually comes off the 2 along the tangent line you drew. Also it matters a lot how much you cut the 2. If you cheat the pocket and send the 2 closer to the 'left' jaw, you hit it fatter and the sidespin gets the result you expected. But if you thin the 2 in and send it very close to the right jaw, it's more likely to die.
Once you get these things you'll start to figure out how to avoid some common problems people have mixing sidespin and speed. One very very common example would be this (lol I'm in a photoshoppy mood):
http://www.jessescornerpocket.com/englishfailure1.jpg