The plate indeed snaps back to a wrong location, but it would still be good to rule out human error and try an updated tutorial or community website. https://www.blender.org/community/

This bug report is a result of opening a 2.79 rig in 2.8x and discovering what broke. The same basic process behind the rig should still work because the same basic features in 2.79 are still in Blender 2.8x -

• Curve Modifier
• Make Vertex Parent
• Transformation Constraint
• Array

The tutorial is still valid, even from 2.79, since the features are still present in 2.8x.

The rig I linked above demonstrates where some bugs might be in the 2.8x version. My guess is that the Transformation Constraint hasn't made the shift to 2.8x unharmed.

I'd be willing to work with the developers to get to the bottom of why this is.

Here is the same file in blender 2.79b:

The result is the same, so it's not a regression.
But I'm not sure if the constraint should behave that way.

Germano, thanks for the confirmation.
I've also now confirmed that the Transform Constraint in 2.79 doesn't work as expected.

I've noticed that it will flip positions when the rotation gets to 180 degrees or -180 degrees.

This makes me think it might be a Euler rotation issue, but I've not had any success changing it.

I analyzed the code and in fact it is a limitation when calculating the euler.
The angle value is obtained by the object's matrix, so the code doesn't know the difference between 361º and 1º for example.

It is a similar problem to T74266
There is no simple solution. And this code is old and not often maintained.