Can you confirm these DEFCON verbs for Twilight Struggle?
You've got them straight.  The rule book uses all of those terms.

The rules are pretty clear on improve, decrease, degrade, and lower:

4.5 A. Improve DEFCON Status: If the DEFCON level is lower than 5, add one to the DEFCON status (towards Peace).
6.3.4 Any Coup attempt in a Battleground country degrades the DEFCON status one level (towards Nuclear War).
8.1.1 DEFCON status measures nuclear tension in the game. The DEFCON level begins the game at its maximum ‘peace’ level of 5. It can go down and back up due to events and actions by the players, but if, at any point, it decreases to , the game ends immediately.

The Extended Playthrough uses increase:

TURN 2
(DEFCON increases to 3, Mil Ops requirements met by both players, no lost points)

[Emphasis added to rule citations]