The reason why this happens is because shape layers are designed so that each shape you create has an independent transform group of properties, with its own position, anchor point, scale, etc. This is actually really cool, since it lets animate multiple shapes in very sophisticated ways, independently from the animation for the main transform properties of the layer itself.
Because of this, the main anchor point for the whole layer may not be centered around the content.
In this case, a very simple solution is: go to the start (in point) of your shape layer, reveal the main Anchor Point (press the A key to do so) in the timeline and drag the values until the shape is centered in the first keyframe for your motion path. This way of adjusting anchor points redefines the "threading" point of your layer relative to the motion path, without affecting the motion path itself (it's the opposite behavior from what the Pan Behind tool does).
Let me know if this is confusing.
It's likely that you transformed your shape path away from the origin (anchor point) of the layer itself.
If you expand all of the options for the shape layer in the timeline, you'll see multiple transformation settings (which may seem redundant, but they are not).
The first one will apply to the shape as it exists within the shape layer.
The second one applies to the layer itself.
If you want your path to line up, you could either center your shape to the anchor point, or move the anchor point to the center of your shape.
You guys are both right. I was accidently moving the shape layer away from the anchor point before creating keyframes. Now I know how to correct that (via moving the anchor point) if it happens again.
Thanks for your help.