The decompression algorithm used for your dive changes with altitude. It is important to understand why.
Altitude training in traditional OW classes was based on tables, which cannot adjust in themselves. That means that the diver had to make adjustments for altitude, and there were two such adjustments.
- Adjust for tissue loading prior to the dive because of increasing altitude by pretending you have already done a dive. This was usually a pretty negligible adjustment, frankly, because the diver had usually been at the new altitude long enough to make it a non-factor.
- Adjust depth using a theoretical depth table. If you were diving to 80 feet at the Blue Hole in New Mexico, the theoretical depth is 96 feet. You would round that to 100 feet and use 100 feet for your table calculations. That would impact your NDL dive time. At sea level at that depth, your maximum time would be 30 minutes; at that altitude it would be 20 minutes.
Computers set to altitude, whether automatically or manually as in this case, will make the same sort of adjustment described in #2 above for you. They can't do #1 above, but, as I said, that is usually not a significant factor at reasonable altitudes. (It is a huge factor in much higher altitudes.)
The reason for the change is the lesser pressure on the surface. As a diver ascends, the diver must make sure the pressure of gases in the body is not too much greater than the surrounding ambient pressure. Decompression algorithms are designed to make sure the ascent allows enough off-gassing for this to be safe. When you are diving, the overwhelming factor in ambient pressure than thus the degree to which you on-gas is the water pressure. If you are diving at at 102 feet of fresh water at sea level, you are under 4 atmospheres of pressure; at the Lake Tahoe, you would be under 3.8 atmospheres of pressure. That is not a lot of difference (95%), so your ongassing would be nearly the same as at sea level. As you ascend, there is still not a whole lot of difference for the first 2/3 of the ascent, but then the air pressure starts to become a bigger portion of ambient pressure. At 34 feet, the sea level ambient pressure is 2 atmospheres; at Lake Tahoe, it is 1.8 atmospheres (90%). At the surface, sea level ambient pressure is 1 atmosphere; at lake Tahoe it is 0.8 Atmospheres (80%).
In summary, when diving at altitude, your body on-gases pretty much the way it does at sea level, and it off-gasses about the same for most of the dive. When you get shallow, things change rapidly, and if you follow a sea level ascent profile, you will be in danger of DCS.
If I were diving at the Blue Hole in New Mexico (about 4,600 feet) with a computer that adjusted for altitude manually, I would set it for the altitude it calls for.