It is certain they would have been using the right fuel.
The best fuel type was limited in supply. So, possible, but by no means certain. Read here about fliegerbenzin and flugbenzin and the other complications that arise in these discussions.
I have read all these threads at the aerodrome, most enlightening, but as you say, no one really knows. Every discussion about whether they used Fliegerbenzin or Flugbenzin and what their properties are are just an educated guess.
The D.IIIau was most likely designed for use with flugbenzin, but no one really knows.
The D.IIIau would most likely run better with Fliegerbenzin, but no one knows if there was enough leftover to fuel the D.IIIau fleet after the D.VIIfs had been fueled.
The tests were probably run just on Flugbenzin, but it looks as though that is probably what they ran on in combat anyway.
The climb tests looks right. The lower figure for the speed test probably comes from the fact that the D.IIIau was not supposed to be run at max throttle below 1,800 meters to prevent detonation.