That situation was pretty common for me while on MDI, except it was not reactive hypoglycemia, it would happen at what appeared to be random times throughout the day.
I would be happily going along at 140-150 then within minutes (sometimes as little as five) I would drop up to 80-100 points! The month before going on the pump I think I had something like 45 or so moderate-severe lows (a couple in the 30s). All of this was happening while my doctor & I continued to reduce my dosage. In a six week period, I reduced my TDD by 35-40% and was still having this effect.
Prior to that six-week period, my BGs were steady as a rock. I could count the number of lows for a full year on one hand!
Been on the pump for about a month now and only had once such occurrence and only two lows total! Which confirmed our suspicion that it was inconsistent absorption of the intermediate-acting insulin combined with a marked increase in insulin sensitivity and/or a reduction in carbohydrate intolerance.
TDD now, on the pump, is less than half what it was before the pump.
And just to complicate things even more, I have noticed that, for me at least, there is not a linear relationship between Carb intake and insulin requirement. If I eat when my BG is in a certain range, my insulin requirement is significantly lower (sometimes by half) than if I eat the exact same meal when my BG is in a higher range.
For example, if my BG is, say, 90 before I eat I need 6 units; but if I have the same meal when my BG is 120 I might need 12-13. That is far more than what one would expect when the correction factor is added in (to reduce the 120 down to my target of 110.)