Questions about calculating caloric deficits

I apologize if any of this sounds silly. I'm brand new to this and completely lost.

I began going to the gym regularly (4 - 6 times a week) early March and was seeing slight results, but hadn't been paying much attention to my diet. I ate out nearly every day due to being a full-time student and working forty hours a week. After doing a juice cleanse for a week early April, I started eating healthier, cooking at home and only having one or two cheat meals, and eyeballing how many calories I was eating. I decided May would be the month I start really counting calories and did it for the first time today. Which is when the confusion set in.
I have read multiple places that losing weight means a deficit of 500 calories a day or 3500 calories a week. MFP calculated I should be eating 1200 calories per day. However, I log my exercise after my food and it ups my remaining calories?

Female
Age: 19
Height: 5'4

CW: 131 lbs
GW: 123 lbs
UGW: 118-120 lbs

BMR: 1433
BMI: 22.5

I suppose my question is, when calculating the deficit, do you account for BMR? Or should I only base it off of how much I burn when I exercise? And why is MFP upping my remaining calories if there's supposed to be a deficit for me to lose weight?