Exercise is very good at reducing insulin resistance - which means that when you exercise enough to trigger that effect, the insulin you have floating about (everyone has background insulin all the time, not just T1s, it is just that the non-T1s generate it themselves) is actually working, like it is supposed to work - so the glucose in your blood finds it easier to get into the cells.
I find that enough exercise, of the right type will effectively drop my bg by at least 1mmol/l, often more. It all depends on how high my insulin resistance was before I started exercise.
When we were on holiday, I would start one of our long, strenuous dog walks at around 5.5mmol, and within half an hour it would have dropped to 4.0mmol. It would stay there for the next few hours I was walking. Steady as a rock, and for a few hours after. No sign of a hypo - no danger of a hypo. Felt great, actually.
Then it would slowly drift back upwards as the day continued. Especially if I ate carbs.
Now, I have a LOT of insulin resistance. The only things that break down IR for me are exercise and prolonged fasting. Since you have lost weight, maybe you have lowered your IR? Plus the effect of exercising may be reducing your IR further, to hitherto unexperienced levels.
But are you feeling bad? Are you actually hypoing if you don't eat those carbs? I don't mean assuming it is a hypo according to your meter and deciding to eat carbs to bring it back up, I mean actually feeling grotty and having a hypo experience? Because if your body is exercising its way to a healthy, normal, non-IR blood glucose level, then that could easily be in the 3s. There are a lot of non-diabetics out there, without insulin resistance, who spend a lot of their time in the 3s. And if you are keto adapted (running dual fuel on fat as well as glucose), then blood glucose in the 3s doesn't necessarily mean you are in trouble. It may just mean that you switch to ketones for muscles and brain, and function perfectly OK.
And if your body, minus insulin resistance, likes to be in the 3s and 4s, when active, and you are feeding it carbs to force the blood glucose back up, then you are also forcing your insulin resistance back up too...
Please note: I am NOT suggesting that you push the boundaries of this, and try to force a hypo, or to see how low you can go, or anything. I am just suggesting that maybe, just maybe, when your body is functioning without insulin resistance, it chooses to run in the 3s, efficiently tucking that glucose into the cells like it is supposed to, and not leaving it in the blood, like happens with a diabetic.
Hope that helps.