Ok I don't use the standard spring strategy, but I will do my best to tell you how its done and where you should be looking at which part.
Ok, first of all you need to identify the different lengths of the springs. A short spring generally lands slightly to the left of DK's left foot or basically flush with the left side of DK's left foot (as it appears on the screen)
A long spring is a spring that bounces flush with the first yellow elevator box.
Once you are in the safe spot above the 2nd yellow elevator box you need to be waiting for a long spring. When a spring makes its first contact with the ground and you can then identify it is a long spring you need to wait until the spring is bouncing directly over marios head. You can actually go slightly before the bottom of the spring becomes parallel with mario's head. At this point you need to start right for the ladder, while watching the next spring, dont look at mario look at or around DK's feet to determine what the next spring will be.
If you have done this correctly, by the time you reach the ladder (and are able to grab it) the next spring will have already identified itself. If this spring is short you need to continue up the ladder. As soon as you have seen that it is short, quickly move your eyes back to mario and make sure he has made the ladder. If mario doesnt quiet make the ladder, (this is very common even with great players) usually you will be just to the left of the ladder and holding up, but since you arent all the way to the ladder you wont climb. If this happens you need to retreat back to the safe spot. Because the time you waste holding up while not climbing is time off your reaction time.
If the next spring comes LONG, you need to retreat. Just practice over and over with save states and you will get it.
So in short: once at the safe spot you need to wait for a long spring to bounce over marios head, it is best to start right just slightly before the spring is parallel to marios head. If the next spring is short keep going and up the ladder. If the next spring is long you need to run back to the safe.
YOUR EYES: once mario is in the safe, you need to be watching the springs not mario. When a long spring comes, quickly look at mario and wait for the spring to bounce over his head, you must do this as the spring is directly over his head of slightly before. As soon as it is straight over marios head run right and QUICKLY move your eyes back to the springs, by the time you see the next spring you will be either at the ladder or almost to the ladder. If then next spring is short quickly look back at mario to make sure he is going up the ladder without stopping short. If the next spring is long look at mario and guide him back to the safe spot and wait again.
Save state practive will help you with timing etc