Your body compensates for the narrowing of the lungs by increasing your breathing rate to maintain as close as possible to full oxygen saturation. The last thing your body wants is to not get enough oxygen, that is fatal very quickly.
You don't want to be in an asthma attack where your O2 drop, that would mean you are having a near-fatal attack.
O2 sats are thing last thing to drop during an asthma attack. They will stay high until you are in really serious shape. If a doctor ever questions your condition ask them what kind of breathing sounds( if any) they are hearing. FEV! is a more accurate diagnostic than o2 sats.
I hope that helps you some.
Take care and feel better.