It depends on the scale of your object and your speed. I suspect you have a larger speed than the one in the demo.
Imagine your speed is 5, and you are 3 units away from your target. This frame, you'll move 5 in the target's direction. Now you're 2 units away, but on the other side. So you'll move 5 units in that direction, and you're back to 3. This is what's happening (although I've exaggerated the values to illustrate).
To fix it, you can either:
1) halt movement within a certain distance of the target. This is fine if your speed is fairly low relative to your object's size. The difference will not be very visible. This is what the example is doing.
2) Ramp down your speed to 0 once you get within a certain distance. This will make it look like the object is braking to a stop at its target.
Either way, just as you choose a speed that works for you, you need to choose values of how close to get and/or how much to slow down.
Lastly, your guess about the "depth" factor is almost right, but it's about the height of your object. Your object's
origin is its center, so if it's taller than 1 unit, then even when it's "at" the target location, the 3D distance between the object and the target is > 0.5.