Adding calories after putting in workout

Assuming you have made a good estimate of what you burn by normal activity (without exercise), MyFitnessPal tries to get you eating less than that, so theoretically, you could lose weight without exercising. So, if you burn calories, and then eat them back, that deficit still exists.

Your goal already has a deficit built into it. If you burn a lot without eating at least some of it back you are not going to be eating enough to fuel your body.

You're supposed to eat them.

If I go to another site and calculate my TDEE (total daily energy expenditure), including my normal daily activity and weekly exercise, I'm told to eat 2300 calories to maintain my current weight. If I wanted to lose one pound a week, I'd take 500 calories off that amount, and eat 1800 calories a day.

MFP doesn't count the exercise you say you'll do into your calorie goal unless and until you do it. To lose one pound a week, MFP would suggest I eat about 1350 calories a day based on my normal daily activity, and once I add my exercise, I would be right back around that 1800 mark.

It's just a different way of getting the same deficit. Some find that "earning" more calories through exercise is more motivating. Some switch to eat a percentage below their TDEE and eat the same amount every day regardless of the amount of exercise.