How does this TDEE stuff work?

If your calculated TDEE is correct, then yes, that is about how much you should be eating for healthy, sustainable weight loss, and eating 1200 will result in hampered metabolic function and loss of lean body mass over time.

Read this for the exhaustive answer:

http://www.myfitnesspal.com/topics/show/912920-in-place-of-a-road-map-3-2013

For your sanity, please try eating a much smaller deficit first to test and see how much weight you are initially losing. You may find you can lose a satisfactory amount while allowing yourself to eat more. If you aren't losing at all after a few consecutive weeks of eating a certain calorie amount, then you can reduce it slightly and continue this strategy until you are losing. People who drop calories too severely too soon do not give themselves much options as to how to adjust their deficits.

Edit: Also, eating a higher amount may let you stumble upon your actual TDEE. Most people do not know how much energy in food they need to eat to maintain weight; without this baseline number, it's very difficult to "guess" the proper deficit. Thus, you'd know what your actual TDEE is (which you can use for later when you bump up calories as you get closer to your goal) and eat more food to reduce fat mass.

Has anyone increased their daily calorie allowance and had increased weight loss? MFP has mine set to 1200, I just worked out my tdee to be 1810 minus the 20% - 1448. I have been feeling frustrated lately because although I'm getting fitter with exercise, I can't really notice any difference in my figure shape. Could that be why?

Increased calories usually results in increased weight loss, after a short period of adjustment. I raised my calories by 50 per week for three weeks. During those three weeks, I maintained weight. Once I had reached my new goal, I lost 2.2 lbs immediately.

bump

MFP does not calculate TDEE. They figure your BMR and your daily activity but not exercise. It is up to you to choose the right level of daily activity including your job. MFP's numbers also depend on what you choose for your weightloss goal. 2lbs a week is too high for a lot of people. THe less you have to lose, the lower your goal should be.
Also, MFP assumes you will log your exercise and tells you to eat those calories back, so even at 1200, on days you exercise you would eat more.

TDEE figures everything, your daily activity and anticipated exercise, then suggests you subtract 20% (which would be closer to 1 lb a week).

I've done it both ways and usually they end up pretty much in the same place.

THIS^^ most people tell MFP they want to lose 2lb a week and then don't bother eating their exercise calories back, Thinking they will not lose weight. MFP has already created a deficit before exercise.

My TDEE is calculated at 1960.

TDEE - 20% = 1568

More than I normally eat, but I'm gonna give it a go!