No real correlation. Carbs should be kept low every day, whatever your overall calorie intake might be. There may be a relation, in that restricting carbohydrate can result in a natural decrease in appetite while weight is being lost. But this may not happen the very first day. You're still likely working through some liver glycogen at this point.

Trust the process, keep the carbs low. Don't worry about calories, high or low, just follow your appetite and see where that gets you. For a lot of people, that gets them where they want to be. The less you're forcing things, the more your just following your appetite, the easier it will be to maintain any losses, since basically you haven't been restricting calories or undereating, you got there by letting your body regulate its own weight relative to your new diet.

Watch out for foods like cheese that are low carb, but seem to cause cravings. Meat and eggs are your friends.