No, MFP is assuming that you'll burn calories at your chosen MFP "Activity Level" for the rest of the day. However, don't pay a lot of attention to your first partial day with your Fitbit. You can rely on the numbers from it more tomorrow.

To see how the adjustment is computed, go to the MFP exercise page (or the Diary on the mobile app) and click on the little 'i' next to the Fitbit Calorie Adjustment (or touch it in the diary) and you'll get a box that shows the math the MFP used to calculate your adjustment.

I would strongly recommend reading the FAQ found in the stickies here. It answers lots of questions that you don't even know you have. Here's a handy link: http://community.myfitnesspal.com/en/discussion/10098937/faq-syncing-logging-food-exercise-calorie-adjustments-activity-levels-accuracy/p1

Fitbit and MFP both use BMR as base.

MFP takes BMR x activity factor for estimated non-exercise daily burn.

Fitbit takes BMR per min x step-based activity level for current daily burn, and depending on setting potential daily burn based on history or indeed BMR.

Depends on what you mean as base?

You are correct - all non-step moving time is given BMR level burn.
That's why it actually has better chance of under-estimating daily burn.
When awake you burn at RMR rate not moving.
When standing not moving you burn even more.
When eating you burn about 10% of calories you ate.

All unaccounted for.