BTW, when the CABIN ALTITUDE warning extinguishes it simply means that you are below 10000 ft regardless of what you have on your altimeters
That really depends on your airplane.
It's possible to have a cabin above or below the indicated or pressure altitude, especially following a rapid descent. Your cabin altitude will generally be close to the indicated altitude, though it could lag by a considerable margin depending on how tight the cabin is, and the nature of the problem. If you happened to have an over pressurization event and shut off the pressurization as a result (and then descended), you may have a cabin below your level-off altitude.
So far as the use of oxygen, the aircraft altitude is irrelevant...the oxygen isn't for the airplane, it's for you, and all that's important to you is cabin altitude.
Descend to a safe altitude and continue on oxygen once the aircraft cabin is at or below that altitude, if the safe altitude is one at which you can get off the oxgyen. A safe altitude doesn't mean a safe cabin altitude however, as the MEA for that area may be too high to permit going off oxygen. There are spots around the world where rushing to 10,000 will hurt you and your crew, and you could very well arrive there even though it's a safe altitude and find the cabin lagging well behind. Descend to the safe altitude, and remove your oxygen mast when it's safe and advisable to do so. That isn't necessarily at the same time you arrive at your descent altitude.