How to edit rounded rectangles' corners

In CS6. If you draw a regular rectangle you can then apply the Round Corners effect.

This remains "Live" and can be adjusted by selecting the Round corners effect in the Appearance panel

Check if you are using the latest version 2015.3.1

You may also check the Show/Hide Corner Widget in the View menu.

To address the title of your question, to have the ability to adjust rounded corners, start either by drawing a square cornered rectangle or by drawing a path with square corners.

If you select a square corned rectangle with the Selection tool, you will see Live Corner widgets. You can drag a widget to adjust the radius on all corners.

If the object has been drawn with a tool other than the Rectangle tool, as long as it has corners, you can select it with the Selection tool. Then switch to the Direct Selection tool to see the corner widgets.

If the object is a rectangle to which Live Corners have been applied, the Transform panel will look like this:

If the object is a path that was not drawn with the rectangle tool, the panel will look like this:

Please select the rounded rectangle in your file and then in the layers panel check what kind of object is listed. Is it a <path> or a <rectangle>?