If his usual readings are around 22 that's very high.
If he feels hypo at 12 that's a false hypo. Because his body is used to running high it incorrectLy thinks dropping to normal readings (and normal would be 4 -8 rather than 12, which remains high) is too low. It's not too low, it's just lower than what he is used to. A hypo is under 4, not under 12. So to get over false hypos he might want to think about gradually stepping down his target ranges and trying not to treat the false hypos, or not to treat them too enthusiastically.
Rapidly dropping from 12 to actually hypo (ie under 4) suggests there might be an issue with too much insulin, either too much bolus insulin (the rapid, before meals), does he work out his bolus dosage by carb counting? or too much basal insulin (insulatard), you can work out your basal dosage with basal testing. Although you aren't really supposed to basal test when hyper up in the 20s.
Run sweet is a good website with info for exercising with type 1 -
http://www.runsweet.com
The main things to think about is: when is he exercising in relation to his last bolus?; if he still has insulin on board (so if it's within 4hrs from his last bolus) he might want to think about reducing that pre-exercise bolus, or taking on some uncovered (ie, not bolused for) carbs before or during the exercise; what is his blood sugar before, during and after exercise? That should give an indication in respect of how much to reduce insulin, or increase carbs.
You say your husband was diagnosed type 1 after abdominal surgery. That wasn't a physical damage to or removal of the pancreas was it? That would make him type 3c and not type 1. A type 3c diabetic has no beta cells and no alpha cells whereas a type 1 diabetic just has no beta cells (although their alpha cells are vulnerable to being worn out). Alpha cells react to hypos by releasing glucagon which tells your liver to release glucose stores. No alpha cells and being type 3c might explain rapid drops from 12 to <4.