Why Does the Centerline Move in Creo Even After Locking It? [See Attached Video]

The "lock" applied to the centerline locks the sketcher constraints active on the object at the time it is locked. Without access to the model, I am not positive, but I do not think that there is any constraint in the horizontal position of that vertical centerline because there is a weak (horizontal) dimension to it relative to the left vertical edge of your sketched rectangle. When you set the rectangle center coincident you will see that weak dimension go away in your video. This behavior supports my hypothesis.

If at the start of this video, you were to apply a strong dimension to control the horizontal position of the centerline then you can lock that dimension and then the rectangle center should snap to the centerline when the coincident constraint is applied to the center point of the rectangle. Try this and report back.

Do not rely on the sketcher intent manager to manage your constraints consistent with your expectations, it is not at all intelligent? Be methodical about your sketch constructs and dimensions.

Lock on a centerline as applied makes it so the centerline can not be "dragged" either inadvertently or on purpose.

It is not locking its position or angle in space. 

To lock it position and/or angle, you will need a dimension or constraint from a reference. Then you can lock the dimension or constraint.

Your references from your model look like they are centered on your block. You can view, change, remove, replace those from within the reference box (or with nothing selected, RMB references) Don't assume Creo selected appropriate references for your sketch.