I have Photoshop CC installed on many machines and the behavior in question happens randomly. Or I keep doing something seamless that I pay attention to that results in this behavior. To recap: I make a selection on a layer, I copy that selection and then I paste. This results in a new layer being created on top of the original layer, composed of that copied selection, but the position of that layer is shifted randomly. I want the newly created layer/pasted selection to appear in the same exact position (on top of the original layer).
If a selection is active, then the paste command will paste in the center of the selection.
If NO selection is active, then the paste will paste in the center of the canvas.
If you want to copy a selection to a new layer, retaining the existing position for the copy, you may find Command/Ctrl+j a better shortcut. It copies, creates a new layer above, and pastes all in 1 step. The menu item for this is located at
Layer > New > Layer via Copy.