working out at eve and then eating back calories

ETA: re: net calories & not getting enough nutrients
In the last 30 days, according to MFP, my net calories have been below 1000 15 days, 1000-1500 9 days, and 1500-2000 6 days.
My actual calories have been right around 1650, except for 6 days when they were higher (usually around 2000).
My doctor is completely satisfied with my progress, my bloodwork is fine, I feel fine, etc.
I've lost 10 lb in the last month, 20 lb in the last 3 months.
Ignore net calories.

It's silly to say ignore net calories, as if it weren't completely dependent on the plan.

Apparently your doctor prefers a method more like the TDEE method (although with a somewhat wacky method of determining calories that wouldn't work for lots of people, although it seems to work fine for you). My guess (giving the doctor some credit) is that this proposed plan would vary depending on the patient. If working with someone who has a higher TDEE and does a lot of hard cardio on a regular basis, that would be built into the plan.

As it is, it sounds like your calories balance out and are probably around a net 1200, which seems to be a doctor favorite (although if your doctor is right it's really a higher net, because of overestimating burn and underestimating calories--this is my personal theory for why doctors so often go lower than necessary, that they don't trust their patients' compliance). Again I expect (and hope) that your doctor had an understanding of your average exercise when making this recommendation, and it seems to be working.

OP's doctor put her on 1200, however (not 1650, like you are eating), thus to say, as if it were some hard and fast rule independent of actual deficit or calories eaten, that one should never eat back calories seems to me irresponsible.

Whether one eats back calories depends on how the deficit is created. If you build it out of exercise and calorie cutting, or if you simply don't think it's going to be that significant, no need to eat it back. If you build it ONLY out of calorie cutting and then add significant exercise on top, you screw it up without changing the calorie cutting part of it. It's just logical.

When I first came here to MFP, I was following a program suggested by my health insurance plan which suggested 1200 calories a day. I logged my food, and I logged my exercise. I was logging 400-500 calorie workouts and I was eating 1200 calories a day. The program did NOT allow for eating back the calories at all. I dropped weight fast, but was tired and groggy. I came here, I set my calories according to TEE - 20% and I eat back about half of my calories throughout the day when I am going to work out. I set my macros and eat inside my macros. In my case, the plan that my medical insurance recommended for me helped me to lose weight but I really don't think it was the healthiest way for me to lose weight.

Now after a workout I drink protein whey and eat a little something even if I don't have much of an appetite. I make sure to drink plenty of water, too, following a work out. For me, I believe that TEE - 20% and staying within my macros is the best and healthiest way to go. It might not be the fastest, but it feels like the healthiest way for me to lose weight.

I pre-log my food and I pre-log my workouts. It works for me. If I change my exercise, I correct what I logged.