Sometimes, doing a large amount of high-intensity exercise while on a ketogenic diet can result in a "Funny turn", i.e. a weird feeling which may include sweating, dizziness & feeling faint.
The good news is that it's harmless, provided you don't faint, fall, and fatally fracture your skull. Stop and sit/lie down until the feeling passes. What's happening?
What isn't happening, is a Somogyi rebound. A Somogyi rebound happens when too much insulin is injected and it's bad because it results in rebound hyperglycaemia.
Did you know that there is insulin, insulin and insulin? According to Insulin: Degradation, "It has been estimated that an insulin molecule produced endogenously by the pancreatic beta cells is degraded within approximately one hour after its initial release into circulation (insulin half-life ~ 4–6 minutes)". According to Insulin: As a medication, injected insulin lingers in the blood for hours for fast-acting and days for slow-acting. This makes an overdose of injected insulin dangerous, as it can linger for long enough to cause fatal hypoglycaemia unless medical help is obtained.
What might be happening, is this: On a ketogenic diet, muscle glycogen stores are "trickle-charged" from blood glucose. High-intensity exercise burns muscle glycogen at a very rapid rate. See It's all in a day's work (as measured in Joules). Muscles can burn carbs at a rate of 4g per minute.
If muscle cells run out of stored glycogen, they become exquisitely sensitive to insulin, and glucose importing processes are up-regulated. There is only ~4.5g of glucose in the blood at any given time, topped-up by the liver & kidneys, and burned by the brain & red blood cells at a rate of less than 4g per hour (if keto-adapted). If muscles start to draw in 4g of glucose per minute, blood glucose can vanish very quickly.
As dropping dead due to running for your life on very little or no food is rather bad, the body has several mechanisms for rapidly raising blood glucose.
From Blood Glucose, Insulin & Diabetes, "When BG falls to ~3.3mmol/L, the pituitary gland kicks-in and secretes ACTH (adrenocorticotropic hormone) which stimulates the release of cortisol from the adrenal cortex. Cortisol further stimulates gluconeogenesis in the liver & kidneys. When BG level falls to ~2mmol/L, the pituitary secretes GH (Growth Hormone) which has an anti-insulin effect." Adrenaline secretion probably increases, too.
A sudden increase in the levels of adrenaline, cortisol & GH in the blood make you sweaty, dizzy & feel faint, so you stop exercising.
How come it's harmless? Glycogen-depleted & exquisitely insulin-sensitive muscles act as a natural blood glucose limiter because they draw in glucose so readily. There is no rebound hyperglycaemia.
This also reduces the "Dawn Phenomenon", another plus point for low-carb diets for diabetics.
See also Can very-low-carb diets impair your mental faculties.