Fitbit is always a replace method - never an add method.

So the 628 from MFP replaced the BMR level burn that was there.

The 271 on Fitbit replaced the 628 from MFP.

Now - purely looking at it in the future you might have hard time knowing which came last and is the used number.

That is odd it didn't update at midnight, mine at least does that.

It may be because Fitbit had a sync value go back to MFP that was 628 higher than last one.

Then it had a replacement and a sync value that was only 271, or rather 357 less than prior time.
But it doesn't push a new figure unless 100 higher than prior time.

That's why I said in post above don't pretend test with big swims at end of day.

It may only do those end of day syncs when the final daily burn is higher than last sync - in this case with the testing you were doing - it'll never send the end of day last sync.

Don't use that as a day to point out to MFP as an example of the issue - not valid and they'll easily find something wrong with it.