Sounds like you may be talking apples and oranges. As I currently understand it (trying to answer the same questions), you have two options:
The first works essentially the same as a closed-circuit rebreather (CCR). The internal pressure drops as the CO2 is absorbed by the scrubber and the replenishment O2 returns the pressure to normal. CCRs actually work off the O2 *partial pressure* but the analogy is conceptually close. Requires an O2 sensor-regulator system and O2 is only added as needed.
The second bleeds *air* (not O2) in as replacement air or at a variable but relatively constant rate, both of which raise the internal pressure and nitrogen content of the breathing mix. It sounds as though Luxury Sub is using an air compressor to vent the excess pressure and nitrogen, making it closer to a semi-closed-circuit rebreather arrangement. A psub version would be an electric air compressor capable of venting through a hull-mounted check-valve at the expected operating pressure.
Warm Regards
Shawn