It happens because the keyboard/mouse buttons appear first in the control configuration. For the controller buttons to appear as hints on screen, you need to swap the order.

From the Options menu, select Controls, then Control Configuration.

Move down to "Jump", press BackSpace twice to delete both the controls.
Press Enter to select, then "A Button" on your controller.
Optional: Press Enter again, then "Space" on your keyboard.
(If you only intend to use a controller, you don't need to re-enter the keyboard/mouse controls.)

Repeat for all the other controls. The full list should look like this:
Up W
Down S
Left A
Right D
Jump A Button/Space
Crouch/Roll B Button/Shift
Grapple X Button/Q
Interact Y Button/E
Shoot Right Trigger/H/L Mouse
Combat Mode Toggle Left Trigger/G/R Mouse
Display HUD Left Shoulder/J
Manual Grab Right Shoulder/Ctrl
Manual Aim Right Stick Button/Z
Pause Esc/Start Button
Inventory Back Button/Tab
Large Medipack DPad Up/B
Small Medipack DPad Down/V
Previous Weapon DPad Left/-
Next Weapon DPad Right/+
Sneak R
Walk Alt
(Note for "Pause": if you delete the control "Esc" you won't be able to get it back without using the "Restore Defaults" option which will reset everything.)