The way the term ketosis is generally used is not quite right.
You generate ketones from fat all the time no matter how high in carb your diet. You will generate more ketones the less carbohydrate you take in, because this increases the demand on fat/ketones for energy. Other ways to increase ketone production include fasting (especially during sleep) and exercise.
A ketogenic diet is one in which a lot of ketones are produced, sometimes to the effect that they cannot all be used and some are excreted in the urine, sweat and breath. This effect is what people like to think of ketosis, but it is not accurate. Once one has fully adapted to metabolizing ketones at a higher rate, aka a ketogenic diet, ketone excretion will decrease as more ketones are metabolized.
Being "in ketosis" is short hand for "excreteing ketones".